Calculus Question

Question

Find the value of this expression: sin 45° sin 15°. The second step =

a. 1/2 [ sin 60° - sin 30°]

b. 1/2 [ cos 60° + cos 30°]

c. 1/2 [ sin 60° + sin 30°]

d. 1/2 [ -cos 60° + cos 30°]

Answer 1

We have the identity

sin x sin y=1/2(cos(x-y)-cos(x+y)).

So, sin 45sin 15=1/2(cos 30-cos 60).