Question 743475
Pick one side and transform it into the other. Once you've chosen a side, you cannot alter the other side at all. I'm going to pick the right side and transform it into the left side.


To do that, multiply top and bottom of the fraction by 1+sin(x) and simplify



[ (1 + sin(x))^2 ]/(cos^2(x)) = (1+sin(x))/(1-sin(x))


[ (1 + sin(x))^2 ]/(cos^2(x)) = [(1+sin(x))(1+sin(x))]/[(1-sin(x))(1+sin(x))]


[ (1 + sin(x))^2 ]/(cos^2(x)) = [(1+sin(x))^2]/[1^2-sin^2(x)]


[ (1 + sin(x))^2 ]/(cos^2(x)) = [(1+sin(x))^2]/[1-sin^2(x)]


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


Both sides are now identical, so this verifies the identity.