Trigonometric Identities. Sum and difference of angle formulas sin(A

Trigonometric Identities.
Sum and difference of angle formulas
sin(A + B)
sin(A − B)
cos(A + B)
cos(A − B)
= sin A cos B + cos A sin B.
= sin A cos B − cos A sin B.
= cos A cos B − sin A sin B.
= cos A cos B + sin A sin B.
tan A + tan B
=
.
1 − tan A tan B
tan A − tan B
.
=
1 + tan A tan B
tan(A + B)
tan(A − B)
Double-angle Formulas
1 − cos 2A
2
1 + cos 2A
2
cos A =
2
1 − cos 2A
2
tan A =
1 + cos 2A
sin2 A =
sin 2A
= 2 sin A cos A
cos 2A
= cos2 A − sin2 A
= 2 cos2 A − 1
tan 2A
= 1 − 2 sin2 A.
2 tan A
=
.
1 − tan2 A
Half-angle Formulas
r
A
sin
2
A
cos
2
=±
r
=±
1 − cos A
.
2
1 + cos A
2
tan
A
2
=
1 − cos A
.
sin A
tan
A
2
=
sin A
.
1 + cos A
Product-to-Sum Formulas
i
1h
cos(A − B) − cos(A + B) .
2
i
1h
cos A cos B =
cos(A − B) + cos(A + B) .
2
i
1h
sin A cos B =
sin(A + B) + sin(A − B) .
2
sin A sin B =
Sum-to-Product Formulas
sin A + sin B
=
2 sin
sin A − sin B
=
2 sin
cos A + cos B
cos A − cos B
A + B 2
A − B cos
2
A + B .
.
2
A − B = 2 cos
cos
.
2
2
A + B A − B = −2 sin
sin
.
2
2
2
A + B cos
A − B