If m = a sec A + b tan A and n = a tan A + b sec A, then prove that :

m² - n² = a² - b²

If x = r cos A cos B, y = r cos A sin B and z = r sin A , show that :

x² + y² + z² = r²

sin² A + sin² (90° - A) is equal to :

1. -1

2. 1

3. 2

4. -2