Q14 of 268 Page 5

Prove the following identities :

Taking LHS

= 3 sec² θ – 4 tan² θ

We know that,

1+ tan² θ = sec² θ

= 3(1+ tan² θ) – 4 tan² θ

= 3 + 3 tan² θ – 4 tan² θ

= 3 – tan² θ

=RHS

Hence Proved

Prove the following identities :

(1+ tan² θ) cos θ. sin θ = tan θ

Prove the following identities :

sin²θ – cos² ϕ = sin²ϕ – cos²θ