determine real numbers a and b so that the expression 8sin^2(theta) + 2cos^2(theta) can be rewritten as (a)sin^2(theta) + b?

Question

If you can help me out on how to start it would be great.

Answer 1

Use the identity:
sin²(x)+cos²(x)=1

In
8sin^2(theta) + 2cos^2(theta)
regroup to get:
6sin^2(theta) + 2(sin^2(theta)+cos^2(theta))
=6sin^2(theta) + 2
QED