Question

What expression is equivalent to 1-2 sin^2x?

I know the answer is 2cos^2x-1, but unsure how to solve it. Do I use the Pythagorean identity to start?

Thanks!

Answer 1

1-2*sin^2 (x) = 2cos^2(x) -1

Explanation:

1-2sin^2(x)

= 1-2(1-cos^2(x)) =2cos^2(x)-1; Pythagorean identity, sin^2(x)=1-cos^2(x)

=1-2+2cos^2(x)=2cos^2(x)-1; distribute

= -1+2cos^2(x)=2cos^2(x) -1; collect and rearrange terms

= 2cos^2(x)-1 = 2cos^2(x)-1