Question

tan(theta)/tan(2theta)-tan(theta)= cos(2theta)

Answer 1

I'll use x for ease of typing

tan(x)/(tan(2x)-tan(x))
tan(x)/((2tanx)/(1-tan^2(x))-tan(x))
tan(x)/((tanx(2/(1-tan^2(x)) - 1)
1/(2/(1-tan^2(x)) - 1)
(1-tan^2(x))/(2 - (1-tan^2(x))
(1-tan^2(x))/(1+tan^2(x))
(1-tan^2(x))/sec^2(x)
(1-tan^2(x))cos^2(x)
cos^2(x)-sin^2(x)
cos(2x)