Question

If cos^2a-sin^2a=tan^2b prove that tan^2a=cos^2b-sin^2b

Answer 1

We know that

cos2A+sin2A=1 ,

and it is given that

cos2A−sin2A=tan2B .

From the above two equations:

sin2Acos2A=12(1−tan2B)=12(1+tan2B)=12sec2B

Now:

sin2Acos2A=tan2A1−tan2Bsec2B=tan2Acos2B−sin2B=tan2A.