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

1 Answer
Oct 4, 2015

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.