ABSTRACT
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.
