Question

Prove the identity:
cos(2theta)/cos squared theta=1-tan squared theta

Answer 1

\[\cos2x/\cos ^{2}x=1-\tan ^{2}x\]
\[(\cos ^{2}x-\sin ^{2}x)/\cos ^{2}x=1-\tan ^{2}x\]
\[\cos ^{2}x/\cos ^{2}x- \sin ^{2}x/\cos ^{2}x= 1-\tan ^{2}x\]
\[1-\tan ^{2}x=1-\tan ^{2}x\]