The value of tan5°tan25°tan45°tan65°tan85° is equal to _________________.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 1.
tan(90° - θ) = cot(θ)
tan5° × tan25° × tan45° × tan65° × tan85°
= tan5° × tan25° × 1 × tan65° × tan85°
= tan5° × tan(25° × cot25° × cot5°
= tan5° × cot5° × tan25° × cot25°
= 1 × 1 = 1