prove that cot x tan 2x-1 =sec 2x

Answer 1

cotx tan2x - 1
= cotx * 2tanx/(1-tan^2x) - 1
= 2/(1 - tan^2x) - 1
= (2 - (1 - tan^2x))/(1 - tan^2x)
= (1 + tan^2x)/(1 - tan^2x)
multiply top and bottom by cos^2x and you have
= (cos^2x + sin^2x)/(cos^2x - sin^2x)
= 1/cos2x
= sec2x