Prove that:
1+cosθ−sin2θsinθ(1+cosθ)=cotθ
1+cosθ−sin2θsinθ(1+cosθ)=sin2θ+cos2θ+cosθ−sin2θsinθ(1+cosθ)=cosθ(cosθ+1)sinθ(1+cosθ)=cosθsinθ=cotθ
Prove the following trigonometric identities:
1+cos θ−sin2θsin θ(1+cos θ)=cot θ
Prove the following trigonometric identities.(i) 1+cosθ+sinθ1+cosθ−sinθ=1+sinθcosθ
(ii) sinθ−cosθ+1sinθ+cosθ−1=1secθ−tanθ
(iii) cosθ−sinθ+1cosθ+sinθ−1=cosecθ+cotθ
(iv) (sinθ+cosθ)(tanθ+cotθ)=secθ+cosecθ