Question

Show that this is an identity by using the definitions of the sum and difference formulas for cosine:

sin(a)sin(b)=1/2[cos(a-b)-cos(a+b)]

And complete these steps:

-Reason
-Apply the definitions of the sum and difference identities for cosine
-Simplify the expressions

Answer 1

½(cos (a - b) - cos (a + b))
= ½(cos a cos b + sin a sin b - (cos a cos b - sin a sin b))
= ½ (cos a cos b + sin a sin b - cos a cos b + sin a sin b)
= ½(2 sin a sin b)
= sin a sin b

Answer 2

Thanks!

Answer 3

How about sin((pi/2)-x)?