Question

Prove that (cos A + sin A – 1)/(cos A – sin A + 1) = cosec A – cot A

Prove that : (1 + 1/tan² θ)(1 + 1/cot² θ) = 1/(sin² θ – sin⁴ θ)

Evaluate : cos 45°/(tan 30° + sin 60°)

If x = a sin θ and y = b cos θ, then b²x² + a²y² is equal to :

Prove the trigonometric identity: √(sec² θ + cosec² θ) = tan θ + cot θ.