Question

Cos2theta(1-costheta) upon sin2theta(1-sintheta) equal1+sin theta upon1+sin2 theta

Answer 1

See the proof below

Explanation:

Reminder :
sin(2θ)=2sinθcosθ
cos(2θ)=2cos2θ−1
tanθ=sinθcosθ
Therefore,
LHS=sinθ+sin2θ1+cosθ+cos2θ
=sinθ+2sinθcosθ1+cosθ+2cos2θ−1
=sinθ(1+2cosθ)cosθ(1+2cosθ)
=tanθ
=RHS
QED