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.

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

$\dfrac{\text{sin}^2 θ}{\text{cos}^2 θ} - \dfrac{1}{ \text{cos}^2 θ}$ = x

Statement (1): x = 1

Statement (2): x = $\dfrac{\text{sin}^2 θ - 1}{{\text{cos}^2 θ}} = \dfrac{-\text{cos}^2 θ}{{\text{cos}^2 θ}}$ = -1

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.

sin A = cos A and tan² A + cot² A + 2

Statement (1): A = 45°

tan² A + cot² A + 2 = 4

Statement (2): sin A = cos A ⇒ A = 45°

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.