Question

Assertion (A): tan 2θ is not defined at θ = 45°.

Reason (R): sin90° = cos 90°.

विकल्प

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

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

• Assertion (A) is true, but Reason (R) is false.

• Assertion (A) is false, but Reason (R) is true.

Answer 1

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

Explanation:

Given:

θ = 45°

tan 2θ = tan (2 × 45°)

tan 2θ = tan 90°

Since tan 90° is not defined, the assertion is true.

sin 90° = 1

cos 90° = 0

1 ≠ 0

So, sin 90° ≠ cos 90° is true.

tan 90° is not defined because tan 90° = `(sin 90°)/(cos 90°) = 1/0`.

A function is undefined when the denominator is zero. While the reason states that sin 90° ≠ cos 90°, the actual reason for tan 90° being undefined is that cos 90° = 0.