TRIGONOMETRIC IDENTITIES tanA = sinA/cosA secA = 1/cosA

TRIGONOMETRIC IDENTITIES
tan A = sin A/ cos A
sec A = 1/ cos A
cosec A = 1/ sin A
cot A = cos A/ sin A = 1/ tan A
sin2 A + cos2 A = 1
sec2 A = 1 + tan2 A
cosec 2 A = 1 + cot2 A
sin(A ± B) = sin A cos B ± cos A sin B
cos(A ± B) = cos A cos B ∓ sin A sin B
tan(A ± B) =
tan A ± tan B
1 ∓ tan A tan B
sin 2A = 2 sin A cos A
cos 2A = cos2 A − sin2 A
= 2 cos2 A − 1
= 1 − 2 sin2 A
tan 2A =
2 tan A
1 − tan2 A
sin 3A = 3 sin A − 4 sin3 A
cos 3A = 4 cos3 A − 3 cos A
tan 3A =
3 tan A − tan3 A
1 − 3 tan2 A
sin A + sin B = 2 sin A+B
cos A−B
2
2
sin A − sin B = 2 cos A+B
sin A−B
2
2
cos A−B
cos A + cos B = 2 cos A+B
2
2
cos A − cos B = −2 sin A+B
sin A−B
2
2
2 sin A cos B = sin(A + B) + sin(A − B)
2 cos A sin B = sin(A + B) − sin(A − B)
2 cos A cos B = cos(A + B) + cos(A − B)
−2 sin A sin B = cos(A + B) − cos(A − B)
a sin x + b cos x = R sin(x + φ), where R =
If t = tan
1
x
2
√
a2 + b2 and cos φ = a/R, sin φ = b/R.
2t
1 − t2
then sin x =
, cos x =
.
1 + t2
1 + t2
cos x = 12 (eix + e−ix ) ;
eix = cos x + i sin x ;
sin x =
1
2i
(eix − e−ix )
e−ix = cos x − i sin x