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.

(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.

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.