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If θ = 9°, find the value of cotθ . cot2θ . cot3θ . cot4θ . cot5θ . cot6θ. cot7θ . cot8θ . cot9θ. |
\(\sqrt {3}\) - 1 1 \(\sqrt {3}\) \(\frac{1}{\sqrt {3}}\) |
1 |
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 |
