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

1 Answer
Jim H
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#.

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