Verify the identity.

Question

(csc(2x) - sin(2x))/cot(2x)=cos(2x)
=csc(2x)/cot(2x) - sin(2x)/cot(2x)
=csc(2x)/cot(2x) - cos(2x)
Is this correct so far? If so then how would I continue? I got stuck on this part...

Answer 1

Oops.
sin/cot = sin*tan = sin^2/cos
csc/cot = 1/sin * sin/cos = 1/cos
You should have said

csc(2x)/cot(2x) - sin(2x)/cot(2x)
= 1/cos(2x) - sin^2(2x)/cos(2x)
= (1-sin^2(2x))/cos(2x)
= cos^2(2x)/cos(2x)
= cos(2x)

or, csc-sin = (1-sin^2)/sin = cos^2/sin = cos * cot