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°.

Express the trigonometric ratios sin A, sec A and tan A in terms of cot A.

Choose the correct option. Justify your choice.

9 sec² A - 9 tan² A =

1. 1

2. 9

3. 8

4. 0

Choose the correct option. Justify your choice.

(1 + tan θ + sec θ)(1 + cot θ - cosec θ) =

1. 0

2. 1

3. 2

4. -1