If sin 2x = 2 sin 45° cos 45°; the value of x is :

1. 45°

2. 90°

3. 30°

4. 60°

For acute angle θ, sec²θ = 1 - tan²θ

Assertion(A): sec²θ = 1 - tan²θ is not a trigonometric identity.

Reason(R): For an acute angle θ, the trigonometric equation is an identity, if it is satisfied for every value of angle θ.

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true and R is correct reason for A.

4. Both A and R are true and R is incorrect reason for A.

cos A = $\dfrac{\sqrt{3}}{2}$ and sin B = $\dfrac{1}{2}$

Assertion (A): tan (A + B) = $\sqrt{3}$

Reason (R): cos A = $\dfrac{\sqrt{3}}{2}$ ⇒ A = 30°

sin B = $\dfrac{1}{2}$ ⇒ B = 30°

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true and R is correct reason for A.

4. Both A and R are true and R is incorrect reason for A.

x = (cosec A + cot A)(1 - cos A)

Assertion (A): x = sin A

Reason (R): x = $\Big(\dfrac{1}{\text{sin A}} + \dfrac{\text{cos A}}{\text{sin A}}\Big)(1 - \text{cos A}) = \dfrac{\text{sin}^2 A}{\text{sin A}} = \text{sin A}$

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true and R is correct reason for A.

4. Both A and R are true and R is incorrect reason for A.