Prove the following by using trigonometric identities:

If sec2A = cosec(A — 42), where 2A is the measure of an acute angle, find the value of A.

If 0 < θ < 90 and secθ = cosec60, find the value of 2cos²θ — 1.

Prove the following by using trigonometric identities:

2sin²θ + 4sec²θ + 5cot²θ + 2cos²θ — 4tan²θ — 5cosec²θ = 1

Prove the following by using trigonometric identities: