Question

(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.

Options

• A is true, R is false.

• A is false, R is true.

• Both A and R are true and R is the correct reason for A.

• Both A and R are true and R is the incorrect reason for A.

Answer 1

A is false, R is true.

Explanation:

Given,

⇒ (1 + tan² A)(1 − sin A)(1 + sin A)

⇒ (1 + tan² A)(1 − sin² A)

⇒ (1 + tan² A)cos² A

⇒ sec² A.cos² A

So, reason (R) are true.

⇒ `1/(cos^2A)` . cos²A

⇒ 1