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

x² + y² + z² = r²

If $\dfrac{\text{cos A}}{\text{cos B}} = m \text{ and } \dfrac{\text{cos A}}{\text{sin B}}$= n,

show that:

(m² + n²) cos² B = n²

In a triangle ABC, sec $\dfrac{C + A}{2}$ is equal to :

1. cosec $\dfrac{B}{2}$

2. sec $\dfrac{B}{2}$

3. cosec $\dfrac{B + A}{2}$

4. none of these

$\dfrac{\text{cot 46°}}{\text{tan 44°}} - 3 \dfrac{\text{sec 20°}}{\text{cosec 70°}}$ + 5 is equal to :

1. -3

2. 4

3. 3

4. -4