Question

Assertion (A): If sec θ + tan θ = a and sec θ – tan θ = b then ab = 1.

Reason (R): sec² θ – tan² θ = 1

Options

• (A) is true and (R) is false.

• (A) is false and (R) is true.

• Both (A) and (R) are true and (R) is the correct explanation of (A).

• Both (A) and (R) are true, but (R) is not the correct explanation of (A).

Answer 1

Both (A) and (R) are true and (R) is the correct explanation of (A).

Explanation:

Given, sec θ + tan θ = a, sec θ – tan θ = b

⇒ ab = (sec θ + tan θ)(sec θ – tan θ)

⇒ ab = sec² θ – tan² θ

⇒ ab = 1

So assertion (A) is true.

We know that,

⇒ sec² θ – tan² θ = 1

This is a fundamental trigonometric identity.

Thus, both (A) and (R) are true and (R) is the correct explanation of (A).