Pre-Calculus help

Question

Verify that 1-cos^2 theta

——————— = Sin^4 theta

1+cos^2 theta

—- is a divider for the fraction

Answer 1

this identity is not true for all thetas

wiil rewrite 1-cos^2 as sin^2

will rewrite sin^4 as (sin^2)(sin^2)

so the original equation becomes (sin^2 x) = (sin^2 x)(sin^2 x). Divide both sides by (sin ^2) leaves sin^2 = 1

sin x = +1, -1

This is only true for pi/2 and 3pi/2 but no other angles