If tanθ + secθ = x, show that sinθ =

If cosθ + sinθ = 1, then prove that cosθ – sin θ = ± 1.

If sinθ + sin²θ = 1, then prove that cos²θ +1 cos⁴θ = 1

If sinθ + cosθ = p and secθ + cosecθ = q, then show q(p²–1) =2p

If x cosθ =a and y = a tanθ, then prove that x²–y²=a²