If (sin θ + cos θ) = √2 cos θ, show that cot θ = (√2 + 1).

If (cosec θ – sin θ) = a³ and (sec θ – cos θ) = b³, prove that a² b² (a² + b²) = 1.

If (2 sin θ + 3 cos θ) = 2, prove that (3 sin θ – 2 cos θ) = ± 3.

If (cos θ + sin θ) = √2sin θ, prove that (sin θ – cos θ) = √2cos θ.

If sec θ + tan θ = p, prove that

(i)

(ii)

(iii)