Cos^2x * csc^2x = csc^2 - 1

Answer 1

Starting with the left-hand side, we will arrive at the right-hand side and thus prove equality. I have included the reasoning/identities on the right-hand side.

cos²x * csc²x = cos²x / sin²x <- csc(x) = 1 / sin(x)

cos²x * csc²x = (1 - sin²x) / sin²x <- cos²x = 1 - sin²x

cos²x * csc²x = 1 / sin²x - 1 <- Distributive Property

cos²x * csc²x = csc²x - 1 <- csc(x) = 1 / sin(x)