7/23/2019 Tom tat cong thuc luong giac

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Cng thc lng gic

1.Cng thc lng gic c bn

2 2

2

2

cos sin 1

11 tg =

cos

+ =

+

2

2

11 cotg =

sin

tg . cotg = 1

+

2. Cng thc cngcos( ) cos .cos sin .sin

cos( ) cos .cos sin .sin

sin( ) sin .cos sin .cos

sin( ) sin .cos sin .cos

+ =

= +

+ = +

=

tg +tgtg( + ) =

1 .

tg tgtg( ) =

1 .

tg tg

tg tg

+

3. Cng thc nhn i, nhn ba

2

sin 2 2sin .cos

22

1

tgtg

tg

=

=

2 2

2

2

cos 2 cos sin

2cos 1

1 2sin

=

=

=

3

3

cos3 4cos 3cos

sin 3 3sin 4sin

=

=

4. Cng thc h bc:

1

sin .cos sin 22

x x x= 2 1 cos 2cos

2

+=

2 1 cos 2sin2

=

2 1 cos 2

1 cos 2tg

=

+

5. Cng thc bin i t!ch th"nh tng

[ ]

[ ]

[ ]

1cos .cos cos( ) cos( )

2

1sin .sin cos( ) cos( )

2

1sin .cos sin( ) sin( )

2

= + +

= +

= + +

#. Cng thc bin i tng th"nh t!ch

cos cos 2cos .cos2 2

cos cos 2sin .sin2 2

sin sin 2sin .cos2 2

sin sin 2cos .sin2 2

+ + =

+ =

+ + =

+ =

2

2

sin( )cos cos

sin( )

cos cos

1 cos 2cos2

1 cos 2sin2

tg tg

tg tg

aa

aa

++ =

=

+ =

=

cosx + sinx = 2sin( x) 2cos( x)4 4

+ = cosx sinx = 2sin( x) 2cos( x)

4 4

= +

4

cos33coscos3

+=

4

3sinsin3sin 3

=