Question

if 2tana=tanb, prove that cos2a = (3+5cos2b)/(5+3cos2b).​

Answer 1

Answer:

Given 2tanA=3tanB

⇒tanA=32tanB

Now

LHS=cos2A

=1−tan2A1+tan2A

=1−94tan2B1+94tan2B

=1−94⋅sin2Bcos2B1+94⋅sin2Bcos2B

=4cos2B−9sin2B4cos2B+9sin2B

=8cos2B−18sin2B8cos2B+18sin2B

=4