Question

Assertion (A): tan 23° tan 45° tan 67° = 1.

Reason (R): tan 23° tan 67° = tan 23° cot(90° − 67°) = tan 23° cot 23° = 1 and tan 45° = 1.

Options

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

• Both A and Rare true but R is the incorrect reason for A

• A is true but R is false.

• A is false but R is true.

Answer 1

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

Explanation:

tan 67° = cot 23°, so tan⁡ 23°⋅ tan⁡ 67° = 1 and tan 45° = 1.

Thus, tan 23° ⋅ tan 45° ⋅ tan 67° = 1.

Therefore, both A and R are true and R is the correct reason for A.