Question

1+cos theta -sin^2 theta / sin theta (1 + cos theta ) = cot theta

Answer 1

1+cosθ-sin²θ/sinθ(1+cosθ)=cotθ
or 1+cosθ-sin²θ+cos²θ-cos²θ/sinθ(1+cosθ)=cotθ
or cosθ+cos²θ/sinθ(1+cosθ)=cotθ
or cosθ(1+cosθ)/sinθ(1+cosθ)=cotθ
or cosθ/sinθ=cotθ
or cotθ=cotθ
We know,cos/sin=cot
So,LHS=RHS,hence,verified

Answer 2

Your answer is in the attachment and pls mark the brainleist