Question

Prove that `(1-sin2x)/(1-cosx)=-cosx`?

Answer 1

This is not an identity, It cannot be proven.

Explanation:

In order to be an identity , for every value of `x` for which the two expressions each evaluate to a number, they must evaluate to the same number.

For some `x`, the two expressions in this question evaluate to different numbers.
For example: if `x=pi/4`, the `2x=pi/2`, so we get

`(1-sin2x)/(1-cosx) = (1-sin(pi/2))/(1-cospi/4) = (1-1)/(1-(sqrt2/2))=0`

`-cosx = -cos(pi/4) = -sqrt2/2`.