# 11x1 t08 02 sum and difference of angles (2010)

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• Sum & Difference of Angles

• Sum & Difference of Anglesy

x

1

• Sum & Difference of Anglesy

x

1

P

• Sum & Difference of Anglesy

x

1

P

• Sum & Difference of Anglesy

x

1

P

1

x

y

• Sum & Difference of Anglesy

x

1

P

1

x

y

cos1x

cosx

cos ,sin

• Sum & Difference of Anglesy

x

1

P

1

x

y

cos1x

cosx sin

1sin

y

y

cos ,sin

• Sum & Difference of Anglesy

x

1

P

1

x

y

cos1x

cosx sin

1sin

y

y

cos ,sin

Q cos ,sin

• Sum & Difference of Anglesy

x

1

P

1

x

y

cos1x

cosx sin

1sin

y

y

cos ,sin

Q cos ,sin

By trigonometry

• Sum & Difference of Anglesy

x

1

P

1

x

y

cos1x

cosx sin

1sin

y

y

cos ,sin

Q cos ,sin

By trigonometry

2 2 21 1 2 1 1 cosPQ

• Sum & Difference of Anglesy

x

1

P

1

x

y

cos1x

cosx sin

1sin

y

y

cos ,sin

Q cos ,sin

By trigonometry

2 2 21 1 2 1 1 cosPQ 2 2 2cosPQ

• Sum & Difference of Anglesy

x

1

P

1

x

y

cos1x

cosx sin

1sin

y

y

cos ,sin

Q cos ,sin

By trigonometry

2 2 21 1 2 1 1 cosPQ 2 2 2cosPQ

By coordinate geometry

• Sum & Difference of Anglesy

x

1

P

1

x

y

cos1x

cosx sin

1sin

y

y

cos ,sin

Q cos ,sin

By trigonometry

2 2 21 1 2 1 1 cosPQ 2 2 2cosPQ

2 22 cos cos sin sinPQ By coordinate geometry

• Sum & Difference of Anglesy

x

1

P

1

x

y

cos1x

cosx sin

1sin

y

y

cos ,sin

Q cos ,sin

By trigonometry

2 2 21 1 2 1 1 cosPQ 2 2 2cosPQ

2 22 cos cos sin sinPQ 2 2 2 2 2cos 2cos cos cos sin 2sin sin sinPQ

By coordinate geometry

• Sum & Difference of Anglesy

x

1

P

1

x

y

cos1x

cosx sin

1sin

y

y

cos ,sin

Q cos ,sin

By trigonometry

2 2 21 1 2 1 1 cosPQ 2 2 2cosPQ

2 22 cos cos sin sinPQ 2 2 2 2 2cos 2cos cos cos sin 2sin sin sinPQ

By coordinate geometry

2 2 2cos cos 2sin sinPQ

• 2 2cos 2 2cos cos 2sin sin

• 2 2cos 2 2cos cos 2sin sin cos cos cos sin sin

• 2 2cos 2 2cos cos 2sin sin cos cos cos sin sin

Replace with

• 2 2cos 2 2cos cos 2sin sin cos cos cos sin sin

Replace with cos cos cos sin sin

• 2 2cos 2 2cos cos 2sin sin cos cos cos sin sin

Replace with cos cos cos sin sin cos cos (even function i.e. )f x f x

• 2 2cos 2 2cos cos 2sin sin cos cos cos sin sin

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

• 2 2cos 2 2cos cos 2sin sin cos cos cos sin sin

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

cos cos cos sin sin

• 2 2cos 2 2cos cos 2sin sin cos cos cos sin sin

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

cos cos cos sin sin

sinsincoscoscos

• 2 2cos 2 2cos cos 2sin sin cos cos cos sin sin

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

cos cos cos sin sin cos, cos, sin, sin

sinsincoscoscos

• 2 2cos 2 2cos cos 2sin sin cos cos cos sin sin

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

cos cos cos sin sin cos, cos, sin, sin

sinsincoscoscos

• 2 2cos 2 2cos cos 2sin sin cos cos cos sin sin

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

cos cos cos sin sin cos, cos, sin, sin

sinsincoscoscos

• 2 2cos 2 2cos cos 2sin sin cos cos cos sin sin

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

cos cos cos sin sin cos, cos, sin, sin

sinsincoscoscos

• 2 2cos 2 2cos cos 2sin sin cos cos cos sin sin

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

cos cos cos sin sin cos, cos, sin, sin

sinsincoscoscos

• 2 2cos 2 2cos cos 2sin sin cos cos cos sin sin

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

cos cos cos sin sin cos, cos, sin, sin

If its not the sine

sinsincoscoscos

• 2 2cos 2 2cos cos 2sin sin cos cos cos sin sin

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

cos cos cos sin sin cos, cos, sin, sin

If its not the sine,its not the sign

sinsincoscoscos

• Replace with 90

• Replace with 90 cos 90 cos 90 cos sin 90 sin

• Replace with 90 cos 90 cos 90 cos sin 90 sin

cos 90 cos 90 cos sin 90 sin

• Replace with 90 cos 90 cos 90 cos sin 90 sin

cos 90 cos 90 cos sin 90 sin sin sin cos cos sin

• Replace with 90 cos 90 cos 90 cos sin 90 sin

cos 90 cos 90 cos sin 90 sin sin sin cos cos sin

Replace with

• Replace with 90 cos 90 cos 90 cos sin 90 sin

cos 90 cos 90 cos sin 90 sin sin sin cos cos sin

Replace with sin sin cos cos sin

• Replace with 90 cos 90 cos 90 cos sin 90 sin

cos 90 cos 90 cos sin 90 sin sin sin cos cos sin

Replace with sin sin cos cos sin sin sin cos cos sin

• Replace with 90 cos 90 cos 90 cos sin 90 sin

cos 90 cos 90 cos sin 90 sin sin sin cos cos sin

Replace with sin sin cos cos sin sin sin cos cos sin

sincoscossinsin

• Replace with 90 cos 90 cos 90 cos sin 90 sin

cos 90 cos 90 cos sin 90 sin sin sin cos cos sin

Replace with sin sin cos cos sin sin sin cos cos sin

sincoscossinsin sin, cos, cos, sin

• Replace with 90 cos 90 cos 90 cos sin 90 sin

cos 90 cos 90 cos sin 90 sin sin sin cos cos sin

Replace with sin sin cos cos sin sin sin cos cos sin

sincoscossinsin sin, cos, cos, sin

• Replace with 90 cos 90 cos 90 cos sin 90 sin

cos 90 cos 90 cos sin 90 sin sin sin cos cos sin

Replace with sin sin cos cos sin sin sin cos cos sin

sincoscossinsin sin, cos, cos, sin

• Replace with 90 cos 90 cos 90 cos sin 90 sin

cos 90 cos 90 cos sin 90 sin sin sin cos cos sin

Replace with sin sin cos cos sin sin sin cos cos sin

sincoscossinsin sin, cos, cos, sin

• Replace with 90 cos 90 cos 90 cos sin 90 sin

cos 90 cos 90 cos sin 90 sin sin sin cos cos sin

Replace with sin sin cos cos sin sin sin cos cos sin

sincoscossinsin sin, cos, cos, sin

• Replace with 90 cos 90 cos 90 cos sin 90 sin

cos 90 cos 90 cos sin 90 sin sin sin cos cos sin

Replace with sin sin cos cos sin sin sin cos cos sin

sincoscossinsin sin, cos, cos, sin

If its the sine

• Replace with 90 cos 90 cos 90 cos sin 90 sin

cos 90 cos 90 cos sin 90 sin sin sin cos cos sin

Replace with sin sin cos cos sin sin sin cos cos sin

sincoscossinsin sin, cos, cos, sin

If its the sine,its the sign

• tan

• tan

sintan

cos

• tan

sintan

cos

sin cos cos sintancos cos sin sin

• tan

sintan

cos

sin cos cos sintancos cos sin