Question

If tan^2 theta = 1+ 2 tan^2 theta, show that Cos 2 theta = 1+ Cos 2 theta

Answer 1

Answer:

given tan2θ=2tan2ϕ+1 

⇒1+tan2θ=2(1+tan2ϕ)⟶(1)

now, cos2θ+sin2ϕ=1+tan2θ1−tan2θ+1−1+tan2ϕ1  

                                    =1+tan2θ1−tan2θ+1−1+tan2θ2,  using equation (1)

                                    =0