If θ = 9°, find the value of cotθ . cot2θ . cot3θ . cot4θ . cot5θ . cot6θ. cot7θ . cot8θ . cot9θ.
Answer & explanation
Correct answer: option 2
Put θ = 9°
⇒ cot9° . cot18° . cot27° . cot36° . cot45° . cot54° . cot63°. cot72° . cot81°
Here, ⇒ (cot A . cot B = 1, when A + B = 90°)
So,
⇒ (cot9° . cot81°) . (cot18° . cot72°) . (cot27° . cot63°) . (cot36° . cot54°) . cot45°
= 1 × 1 × 1 × 1 × 1 = 1