Question

How do you prove that `(sec^2theta)/2 = (2-2cos^2theta)csc^2(2theta)`?

Answer 1

see below

Explanation:

RHS =`2(1-cos^2theta)*1/sin^2(2theta)`
=`2(1-cos^2theta)*1/(4sin^2theta*cos^2theta)`
=`2(sin^2theta)*1/(4sin^2theta*cos^2theta)`
=`sec^2theta/2` = LHS