The value of tan 25°.tan 35°.tan 45°.tan 55°.tan 65° is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 1.
tan 25°.tan 35°.tan 45°.tan 55°.tan 65°
⇒ tan (90° - 65°) × tan (90° - 55°) × 1 × tan 55° × tan 65°
⇒ cot 65° × cot 55° × 1 × tan 55° × tan 65°
⇒ cot 55° × (1/cot 55°) × cot 65° × (1/cot 65°)
⇒ 1