6. Five mark example problems I

1. If \(cosec \ \theta + cot \ \theta = P\), then prove that \(cos \ \theta = \frac{P^2 - 1}{P^2 + 1}\).

 

2. Prove that \(tan^2 \ A - tan^2 \ B = \frac{sin^2 \ A - sin^2 \ B}{cos^2 \ A \ cos^2 \ B}\).

 

3. Prove that \(\left(\frac{cos^3 \ A - sin^3 \ A}{cos \ A - sin \ A} \right) - \left(\frac{cos^3 \ A + sin^3 \ A}{cos \ A + sin \ A} \right) = 2 \ sin \ A \ cos \ A\)