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