Prove the following identities :(1+ tan2 θ) cos θ. sin θ = tan θ

Taking LHS = (1+ tan2 θ) cos θ sin θ= (sec2 θ) cos θ sin θ [∵ 1+ tan2 θ = sec2 θ]= tan θ =RHSHence Proved

Q14 of 268 Page 5

Prove the following identities :
(1+ tan² θ) cos θ. sin θ = tan θ

Taking LHS = (1+ tan² θ) cos θ sin θ

= (sec² θ) cos θ sin θ [∵ 1+ tan² θ = sec² θ]

= tan θ

=RHS

Hence Proved

Prove the following identities :

sin²θ – cos² ϕ = sin²ϕ – cos²θ

Prove the following identities :