Use the power-reducing formulas to rewrite tan^2x/sin^2x in terms of the first power of the cosine

Answer 1

Hi Ashley B.,

For tan²(x) we have the half angle identity, tan²(x) = [1 - cos(2x)]/[1 + cos(2x)].

And for sin²(x) we have the half angle identity sin²(x) = [1 - cos(2x)]/2.

Therfore:

tan²(x)/sin²(x) = {[1 - cos(2x)]/[1 + cos(2x)]} / {[1 - cos(2x)]/2}

= {[1 - cos(2x)]/[1 + cos(2x)]} * {2/[1 - cos(2x)}

= 2 / [1 + cos(2x)]

I hope this helps, Joe.