Prove the following trigonometric identities:

Prove the following identities :

tan⁴θ + tan²θ = sec⁴θ – sec²θ

Prove the following identities :

sin² θ(1+ cot² θ) = 1

Prove the following identities :

cos² A (tan² A+1) = 1

If sin 77° = x, then write the value of cos 77^o in terms of x.

If cos55° = x², then write the value of sin 55^o in terms of x.

If cos40^o = p, then write the value of sin 40^o in terms of p.