Question

cos2theta/1+sin2theta = tan(45-theta) prove

Answer 1

tan(45-a)=tan45+tana/1-tan45 tana(let us consider theta = a)

=1+tan a/1-tan a(tan a=sin a/cos a)

=cos a+sin a/cos a-sin a

=cos^2 a-sin^2 a/(cos a-sin a)^2(by rationalizing)

cos 2a/cos^2 a+sin^2 a-2 sin a cos a(cos^2 a+sin^2 a=1,sin2a=2 sina cos a)

cos2a/1-sin2a