Choose the correct option and justify your choice :

$\dfrac{\text{1 - tan}^2 45°}{\text{1 + tan}^2 45°} =$

1. tan 90°

2. 1

3. sin 45°

4. 0

Choose the correct option and justify your choice :

sin 2A = 2 sin A is true when A =

1. 0°

2. 30°

3. 45°

4. 60°

If tan (A + B) = $\sqrt{3}$ and tan (A – B) = $\dfrac{1}{\sqrt{3}}$; 0° < A + B ≤ 90°; A > B, find A and B.

State whether the following are true or false. Justify your answer.

(i) sin (A + B) = sin A + sin B.

(ii) The value of sin θ increases as θ increases.

(iii) The value of cos θ increases as θ increases.

(iv) sin θ = cos θ for all values of θ.

(v) cot A is not defined for A = 0°.