chapter  18
Compound angles
Pages 13

The compound-angle formulae are true for all values of A and B, and by substituting values of A and B into the formulae they may be shown to be true.

Problem 1. Expand and simplify the following expressions: (a) sin(π +α) (b) −cos(90◦ +β) (c) sin(A − B) − sin(A + B)

(a) sin(π +α) = sin π cos α+ cos π sin α (from the formula for sin (A + B))

= (0)(cos α) + (−1) sin α = −sin α (b) −cos (90◦ + β)

= −[cos 90◦ cos β − sin 90◦ sin β] = −[(0)(cos β) − (1) sin β] = sin β

(c) sin(A − B) − sin(A + B) = [sin A cos B − cos A sin B]

− [sin A cos B + cos A sin B] = −2cos A sin B

Problem 2. Prove that

cos(y − π) + sin (

y + π 2

) = 0.