(1 + tan² A)(1 - sin A)(1 + sin A)

Assertion(A): The value of given trigonometric expression is 0.

Reason(R): The given expression is equal to sec² A.cos² 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.

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.

$\dfrac{1 - \text{sin A}}{\text{cos A}}$ = sec A - tan A

Statement (1): $\dfrac{1 - \text{sin A}}{\text{cos A}}$ = sec A - tan A

$\Rightarrow \dfrac{1 + \text{sin A}}{\text{cos A}}$ = sec A + tan A

Statement (2): $\dfrac{1 - \text{sin A}}{\text{cos A}} - \dfrac{1 + \text{sin A}}{\text{cos A}}$ = 2sec A

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.

$\text{cos}^2 θ + \dfrac{1}{1 + {\text{cot}^2 θ}}$ = x

Statement (1): x = 1

Statement (2): x = $\text{cos}^2 θ + \dfrac{1}{{\text{cosec}^2 θ}}$ = cos² θ + sin² θ

1. Both the statement are true.

2. Both the statement are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.