Prove the following by using trigonometric identities:

tan²A — tan²B =

Prove the following by using trigonometric identities:

Prove the following by using trigonometric identities:

sin⁴θ – cos⁴θ = sin²θ – cos²θ = 2sin²θ – 1 = 1 – 2 cos²θ.

Prove the following by using trigonometric identities:

2(sin⁶θ + cos⁶θ) — 3(sin⁴θ + cos⁴θ) + 1 = 0

If sinθ + cosθ = p and secθ + cosecθ = q, show that q(p² — 1) = 2p.