11X1 T07 02 sum & difference of angles (2011)

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<ul><li><p>Sum &amp; Difference of Angles</p></li><li><p>Sum &amp; Difference of Anglesy</p><p>x</p><p>1</p></li><li><p>Sum &amp; Difference of Anglesy</p><p>x</p><p>1</p><p>P</p></li><li><p>Sum &amp; Difference of Anglesy</p><p>x</p><p>1</p><p>P</p></li><li><p>Sum &amp; Difference of Anglesy</p><p>x</p><p>1</p><p>P</p><p> 1</p><p>x</p><p>y</p></li><li><p>Sum &amp; Difference of Anglesy</p><p>x</p><p>1</p><p>P</p><p> 1</p><p>x</p><p>y</p><p>cos1x </p><p>cosx </p><p> cos ,sin </p></li><li><p>Sum &amp; Difference of Anglesy</p><p>x</p><p>1</p><p>P</p><p> 1</p><p>x</p><p>y</p><p>cos1x </p><p>cosx sin</p><p>1sin</p><p>y</p><p>y</p><p> cos ,sin </p></li><li><p>Sum &amp; Difference of Anglesy</p><p>x</p><p>1</p><p>P</p><p> 1</p><p>x</p><p>y</p><p>cos1x </p><p>cosx sin</p><p>1sin</p><p>y</p><p>y</p><p> cos ,sin </p><p> Q cos ,sin </p></li><li><p>Sum &amp; Difference of Anglesy</p><p>x</p><p>1</p><p>P</p><p> 1</p><p>x</p><p>y</p><p>cos1x </p><p>cosx sin</p><p>1sin</p><p>y</p><p>y</p><p> cos ,sin </p><p> Q cos ,sin </p><p>By trigonometry</p></li><li><p>Sum &amp; Difference of Anglesy</p><p>x</p><p>1</p><p>P</p><p> 1</p><p>x</p><p>y</p><p>cos1x </p><p>cosx sin</p><p>1sin</p><p>y</p><p>y</p><p> cos ,sin </p><p> Q cos ,sin </p><p>By trigonometry</p><p> 2 2 21 1 2 1 1 cosPQ </p></li><li><p>Sum &amp; Difference of Anglesy</p><p>x</p><p>1</p><p>P</p><p> 1</p><p>x</p><p>y</p><p>cos1x </p><p>cosx sin</p><p>1sin</p><p>y</p><p>y</p><p> cos ,sin </p><p> Q cos ,sin </p><p>By trigonometry</p><p> 2 2 21 1 2 1 1 cosPQ 2 2 2cosPQ </p></li><li><p>Sum &amp; Difference of Anglesy</p><p>x</p><p>1</p><p>P</p><p> 1</p><p>x</p><p>y</p><p>cos1x </p><p>cosx sin</p><p>1sin</p><p>y</p><p>y</p><p> cos ,sin </p><p> Q cos ,sin </p><p>By trigonometry</p><p> 2 2 21 1 2 1 1 cosPQ 2 2 2cosPQ </p><p>By coordinate geometry</p></li><li><p>Sum &amp; Difference of Anglesy</p><p>x</p><p>1</p><p>P</p><p> 1</p><p>x</p><p>y</p><p>cos1x </p><p>cosx sin</p><p>1sin</p><p>y</p><p>y</p><p> cos ,sin </p><p> Q cos ,sin </p><p>By trigonometry</p><p> 2 2 21 1 2 1 1 cosPQ 2 2 2cosPQ </p><p> 2 22 cos cos sin sinPQ By coordinate geometry</p></li><li><p>Sum &amp; Difference of Anglesy</p><p>x</p><p>1</p><p>P</p><p> 1</p><p>x</p><p>y</p><p>cos1x </p><p>cosx sin</p><p>1sin</p><p>y</p><p>y</p><p> cos ,sin </p><p> Q cos ,sin </p><p>By trigonometry</p><p> 2 2 21 1 2 1 1 cosPQ 2 2 2cosPQ </p><p> 2 22 cos cos sin sinPQ 2 2 2 2 2cos 2cos cos cos sin 2sin sin sinPQ </p><p>By coordinate geometry</p></li><li><p>Sum &amp; Difference of Anglesy</p><p>x</p><p>1</p><p>P</p><p> 1</p><p>x</p><p>y</p><p>cos1x </p><p>cosx sin</p><p>1sin</p><p>y</p><p>y</p><p> cos ,sin </p><p> Q cos ,sin </p><p>By trigonometry</p><p> 2 2 21 1 2 1 1 cosPQ 2 2 2cosPQ </p><p> 2 22 cos cos sin sinPQ 2 2 2 2 2cos 2cos cos cos sin 2sin sin sinPQ </p><p>By coordinate geometry</p><p>2 2 2cos cos 2sin sinPQ </p></li><li><p> 2 2cos 2 2cos cos 2sin sin </p></li><li><p> 2 2cos 2 2cos cos 2sin sin cos cos cos sin sin </p></li><li><p> 2 2cos 2 2cos cos 2sin sin cos cos cos sin sin </p><p>Replace with </p></li><li><p> 2 2cos 2 2cos cos 2sin sin cos cos cos sin sin </p><p>Replace with cos cos cos sin sin </p></li><li><p> 2 2cos 2 2cos cos 2sin sin cos cos cos sin sin </p><p>Replace with cos cos cos sin sin cos cos (even function i.e. )f x f x </p></li><li><p> 2 2cos 2 2cos cos 2sin sin cos cos cos sin sin </p><p>Replace with cos cos cos sin sin cos cos (even function i.e. )f x f x sin sin (odd function i.e. )f x f x </p></li><li><p> 2 2cos 2 2cos cos 2sin sin cos cos cos sin sin </p><p>Replace with cos cos cos sin sin cos cos (even function i.e. )f x f x sin sin (odd function i.e. )f x f x </p><p> cos cos cos sin sin </p></li><li><p> 2 2cos 2 2cos cos 2sin sin cos cos cos sin sin </p><p>Replace with cos cos cos sin sin cos cos (even function i.e. )f x f x sin sin (odd function i.e. )f x f x </p><p> cos cos cos sin sin </p><p> sinsincoscoscos </p></li><li><p> 2 2cos 2 2cos cos 2sin sin cos cos cos sin sin </p><p>Replace with cos cos cos sin sin cos cos (even function i.e. )f x f x sin sin (odd function i.e. )f x f x </p><p> cos cos cos sin sin cos, cos, sin, sin</p><p> sinsincoscoscos </p></li><li><p> 2 2cos 2 2cos cos 2sin sin cos cos cos sin sin </p><p>Replace with cos cos cos sin sin cos cos (even function i.e. )f x f x sin sin (odd function i.e. )f x f x </p><p> cos cos cos sin sin cos, cos, sin, sin</p><p> sinsincoscoscos </p></li><li><p> 2 2cos 2 2cos cos 2sin sin cos cos cos sin sin </p><p>Replace with cos cos cos sin sin cos cos (even function i.e. )f x f x sin sin (odd function i.e. )f x f x </p><p> cos cos cos sin sin cos, cos, sin, sin</p><p> sinsincoscoscos </p></li><li><p> 2 2cos 2 2cos cos 2sin sin cos cos cos sin sin </p><p>Replace with cos cos cos sin sin cos cos (even function i.e. )f x f x sin sin (odd function i.e. )f x f x </p><p> cos cos cos sin sin cos, cos, sin, sin</p><p> sinsincoscoscos </p></li><li><p> 2 2cos 2 2cos cos 2sin sin cos cos cos sin sin </p><p>Replace with cos cos cos sin sin cos cos (even function i.e. )f x f x sin sin (odd function i.e. )f x f x </p><p> cos cos cos sin sin cos, cos, sin, sin</p><p> sinsincoscoscos </p></li><li><p> 2 2cos 2 2cos cos 2sin sin cos cos cos sin sin </p><p>Replace with cos cos cos sin sin cos cos (even function i.e. )f x f x sin sin (odd function i.e. )f x f x </p><p> cos cos cos sin sin cos, cos, sin, sin</p><p>If its not the sine</p><p> sinsincoscoscos </p></li><li><p> 2 2cos 2 2cos cos 2sin sin cos cos cos sin sin </p><p>Replace with cos cos cos sin sin cos cos (even function i.e. )f x f x sin sin (odd function i.e. )f x f x </p><p> cos cos cos sin sin cos, cos, sin, sin</p><p>If its not the sine,its not the sign</p><p> sinsincoscoscos </p></li><li><p>Replace with 90 </p></li><li><p>Replace with 90 cos 90 cos 90 cos sin 90 sin </p></li><li><p>Replace with 90 cos 90 cos 90 cos sin 90 sin </p><p> cos 90 cos 90 cos sin 90 sin </p></li><li><p>Replace with 90 cos 90 cos 90 cos sin 90 sin </p><p> cos 90 cos 90 cos sin 90 sin sin sin cos cos sin </p></li><li><p>Replace with 90 cos 90 cos 90 cos sin 90 sin </p><p> cos 90 cos 90 cos sin 90 sin sin sin cos cos sin </p><p>Replace with </p></li><li><p>Replace with 90 cos 90 cos 90 cos sin 90 sin </p><p> cos 90 cos 90 cos sin 90 sin sin sin cos cos sin </p><p>Replace with sin sin cos cos sin </p></li><li><p>Replace with 90 cos 90 cos 90 cos sin 90 sin </p><p> cos 90 cos 90 cos sin 90 sin sin sin cos cos sin </p><p>Replace with sin sin cos cos sin sin sin cos cos sin </p></li><li><p>Replace with 90 cos 90 cos 90 cos sin 90 sin </p><p> cos 90 cos 90 cos sin 90 sin sin sin cos cos sin </p><p>Replace with sin sin cos cos sin sin sin cos cos sin </p><p> sincoscossinsin </p></li><li><p>Replace with 90 cos 90 cos 90 cos sin 90 sin </p><p> cos 90 cos 90 cos sin 90 sin sin sin cos cos sin </p><p>Replace with sin sin cos cos sin sin sin cos cos sin </p><p> sincoscossinsin sin, cos, cos, sin</p></li><li><p>Replace with 90 cos 90 cos 90 cos sin 90 sin </p><p> cos 90 cos 90 cos sin 90 sin sin sin cos cos sin </p><p>Replace with sin sin cos cos sin sin sin cos cos sin </p><p> sincoscossinsin sin, cos, cos, sin</p></li><li><p>Replace with 90 cos 90 cos 90 cos sin 90 sin </p><p> cos 90 cos 90 cos sin 90 sin sin sin cos cos sin </p><p>Replace with sin sin cos cos sin sin sin cos cos sin </p><p> sincoscossinsin sin, cos, cos, sin</p></li><li><p>Replace with 90 cos 90 cos 90 cos sin 90 sin </p><p> cos 90 cos 90 cos sin 90 sin sin sin cos cos sin </p><p>Replace with sin sin cos cos sin sin sin cos cos sin </p><p> sincoscossinsin sin, cos, cos, sin</p></li><li><p>Replace with 90 cos 90 cos 90 cos sin 90 sin </p><p> cos 90 cos 90 cos sin 90 sin sin sin cos cos sin </p><p>Replace with sin sin cos cos sin sin sin cos cos sin </p><p> sincoscossinsin sin, cos, cos, sin</p></li><li><p>Replace with 90 cos 90 cos 90 cos sin 90 sin </p><p> cos 90 cos 90 cos sin 90 sin sin sin cos cos sin </p><p>Replace with sin sin cos cos sin sin sin cos cos sin </p><p> sincoscossinsin sin, cos, cos, sin</p><p>If its the sine</p></li><li><p>Replace with 90 cos 90 cos 90 cos sin 90 sin </p><p> cos 90 cos 90 cos sin 90 sin sin sin cos cos sin </p><p>Replace with sin sin cos cos sin sin sin cos cos sin </p><p> sincoscossinsin sin, cos, cos, sin</p><p>If its the sine,its the sign</p></li><li><p> tan </p></li><li><p> tan </p><p>sintan</p><p>cos </p></li><li><p> tan </p><p>sintan</p><p>cos </p><p> sin cos cos sintancos cos sin sin</p></li><li><p> tan </p><p>sintan</p><p>cos </p><p> sin cos cos sintancos cos sin sin</p><p> sin cos cos sincos cos cos costan cos cos sin sincos cos cos cos</p></li><li><p> tan </p><p>sintan</p><p>cos </p><p> sin cos cos sintancos cos sin sin</p><p> sin cos cos sincos cos cos costan cos cos sin sincos cos cos cos</p><p> tan tantan1 tan tan</p></li><li><p> tan </p><p>sintan</p><p>cos </p><p> sin cos cos sintancos cos sin sin</p><p> sin cos cos sincos cos cos costan cos cos sin sincos cos cos cos</p><p> tan tantan1 tan tan</p><p>Replace with </p></li><li><p> tan </p><p>sintan</p><p>cos </p><p> sin cos cos sintancos cos sin sin</p><p> sin cos cos sincos cos cos costan cos cos sin sincos cos cos cos</p><p> tan tantan1 tan tan</p><p>Replace with </p><p>tan tantan</p><p>1 tan tan </p></li><li><p> tan </p><p>sintan</p><p>cos </p><p> sin cos cos sintancos cos sin sin</p><p> sin cos cos sincos cos cos costan cos cos sin sincos cos cos cos</p><p> tan tantan1 tan tan</p><p>Replace with </p><p>tan tantan</p><p>1 tan tan tan tan </p><p> (odd function i.e. )f x f x </p></li><li><p> tan </p><p>sintan</p><p>cos </p><p> sin cos cos sintancos cos sin sin</p><p> sin cos cos sincos cos cos costan cos cos sin sincos cos cos cos</p><p> tan tantan1 tan tan</p><p>Replace with </p><p>tan tantan</p><p>1 tan tan tan tan </p><p> (odd function i.e. )f x f x tan tantan1 tan tan</p></li><li><p>tantan1tantantan </p></li><li><p>tan plus tan</p><p>tantan1tantantan </p></li><li><p>tan plus tan</p><p>on one minus tan, tan</p><p>tantan1tantantan </p></li><li><p>tan plus tan</p><p>on one minus tan, tan</p><p>tantan1tantantan </p><p>Sum and Difference of Angles</p></li><li><p>tan plus tan</p><p>on one minus tan, tan</p><p>tantan1tantantan </p><p>Sum and Difference of Angles</p><p> sincoscossinsin </p></li><li><p>tan plus tan</p><p>on one minus tan, tan</p><p>tantan1tantantan </p><p>Sum and Difference of Angles</p><p> sincoscossinsin sinsincoscoscos </p></li><li><p>tan plus tan</p><p>on one minus tan, tan</p><p>tantan1tantantan </p><p>Sum and Difference of Angles</p><p> sincoscossinsin sinsincoscoscos </p><p>tantan1tantantan </p></li><li><p> e.g. i Expand cos 2 3 </p></li><li><p> e.g. i Expand cos 2 3 cos 2 3 cos 2 cos3 sin 2 sin 3 </p></li><li><p> e.g. i Expand cos 2 3 cos 2 3 cos 2 cos3 sin 2 sin 3 </p><p>tan 20 tan10(ii) Simplify 1 tan 20 tan10</p></li><li><p> e.g. i Expand cos 2 3 cos 2 3 cos 2 cos3 sin 2 sin 3 </p><p>tan 20 tan10(ii) Simplify 1 tan 20 tan10</p><p> tan 20 tan10 tan 20 101 tan 20 tan10</p></li><li><p> e.g. i Expand cos 2 3 cos 2 3 cos 2 cos3 sin 2 sin 3 </p><p>tan 20 tan10(ii) Simplify 1 tan 20 tan10</p><p> tan 20 tan10 tan 20 101 tan 20 tan10</p><p>tan30 </p></li><li><p> e.g. i Expand cos 2 3 cos 2 3 cos 2 cos3 sin 2 sin 3 </p><p>tan 20 tan10(ii) Simplify 1 tan 20 tan10</p><p> tan 20 tan10 tan 20 101 tan 20 tan10</p><p>tan30 13</p></li><li><p> e.g. i Expand cos 2 3 cos 2 3 cos 2 cos3 sin 2 sin 3 </p><p>tan 20 tan10(ii) Simplify 1 tan 20 tan10</p><p> tan 20 tan10 tan 20 101 tan 20 tan10</p><p>tan30 13</p><p>(iii) Find the exact value of sin15</p></li><li><p> e.g. i Expand cos 2 3 cos 2 3 cos 2 cos3 sin 2 sin 3 </p><p>tan 20 tan10(ii) Simplify 1 tan 20 tan10</p><p> tan 20 tan10 tan 20 101 tan 20 tan10</p><p>tan30 13</p><p>(iii) Find the exact value of sin15</p><p> sin15 sin 45 30 </p></li><li><p> e.g. i Expand cos 2 3 cos 2 3 cos 2 cos3 sin 2 sin 3 </p><p>tan 20 tan10(ii) Simplify 1 tan 20 tan10</p><p> tan 20 tan10 tan 20 101 tan 20 tan10</p><p>tan30 13</p><p>(iii) Find the exact value of sin15</p><p> sin15 sin 45 30 sin 45 cos30 cos 45 sin30 </p></li><li><p> e.g. i Expand cos 2 3 cos 2 3 cos 2 cos3 sin 2 sin 3 </p><p>tan 20 tan10(ii) Simplify 1 tan 20 tan10</p><p> tan 20 tan10 tan 20 101 tan 20 tan10</p><p>tan30 13</p><p>(iii) Find the exact value of sin15</p><p> sin15 sin 45 30 sin 45 cos30 cos 45 sin30 </p><p>1 3 1 12 22 2</p></li><li><p> e.g. i Expand cos 2 3 cos 2 3 cos 2 cos3 sin 2 sin 3 </p><p>tan 20 tan10(ii) Simplify 1 tan 20 tan10</p><p> tan 20 tan10 tan 20 101 tan 20 tan10</p><p>tan30 13</p><p>(iii) Find the exact value of sin15</p><p> sin15 sin 45 30 sin 45 cos30 cos 45 sin30 </p><p>1 3 1 12 22 2</p><p> 3 1</p><p>2 2</p></li><li><p> 2 1iv If sin and cos , find sin3 4</p></li><li><p> 2 1iv If sin and cos , find sin3 4</p><p>23</p><p>5</p></li><li><p> 2 1iv If sin and cos , find sin3 4</p><p>23</p><p>5</p><p>1</p><p>4 15</p></li><li><p> 2 1iv If sin and cos , find sin3 4</p><p>23</p><p>5</p><p>1</p><p>4 15</p><p> sin sin cos cos sin </p></li><li><p> 2 1iv If sin and cos , find sin3 4</p><p>23</p><p>5</p><p>1</p><p>4 15</p><p> sin sin cos cos sin 2 1 5 153 4 3 4</p></li><li><p> 2 1iv If sin and cos , find sin3 4</p><p>23</p><p>5</p><p>1</p><p>4 15</p><p> sin sin cos cos sin 2 1 5 153 4 3 4</p><p> 2 5 3</p><p>12</p></li><li><p> 2 1iv If sin and cos , find sin3 4</p><p>23</p><p>5</p><p>1</p><p>4 15</p><p> sin sin cos cos sin 2 1 5 153 4 3 4</p><p> 2 5 3</p><p>12</p><p>Exercise 14D; 1ade, 2bce, 5ac, 7, 9ac, 10ac, 12, 13ac, 16ab, 17, 23</p><p>Slide Number 1Slide Number 2Slide Number 3Slide Number 4Slide Number 5Slide Number 6Slide Number 7Slide Number 8Slide Number 9Slide Number 10Slide Number 11Slide Number 12Slide Number 13Slide Number 14Slide Number 15Slide Number 16Slide Number 17Slide Number 18Slide Number 19Slide Number 20Slide Number 21Slide Number 22Slide Number 23Slide Number 24Slide Number 25Slide Number 26Slide Number 27Slide Number 28Slide Number 29Slide Number 30Slide Number 31Slide Number 32Slide Number 33Slide Number 34Slide Number 35Slide Number 36Slide Number 37Slide Number 38Slide Number 39Slide Number 40Slide Number 41Slide Number 42Slide Number 43Slide Number 44Slide Number 45Slide Number 46Slide Number 47Slide Number 48Slide Number 49Slide Number 50Slide Number 51Slide Number 52Slide Number 53Slide Number 54Slide Number 55Slide Number 56Slide Number 57Slide Number 58Slide Number 59Slide Number 60Slide Number 61Slide Number 62Slide Number 63Slide Number 64Slide Number 65Slide Number 66Slide Number 67Slide Number 68Slide Number 69Slide Number 70Slide Number 71Slide Number 72Slide Number 73Slide Number 74Slide Number 75Slide Number 76Slide Number 77Slide Number 78Slide Number 79</p></li></ul>