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If θ = 9°, then what is the value of  Cot θ cot 2 θ cot 3 θ cot 4 θ cot 5 θ cot 6 θ cot 7 θ cot 8 θ cot 9 θ ?

If θ = 9°, then what is the value of  Cot θ cot 2 θ cot 3 θ cot 4 θ cot 5 θ cot 6 θ cot 7 θ cot 8 θ cot 9 θ ? Correct Answer 1

Given that,

θ = 9°

10θ = 90°

Given expression,

Cotθ.Cot2θ.Cot3θ.Cot4θ.Cot5θ.Cot6θ.Cot7θ.Cot8θ.Cot9θ

⇒ Cotθ.Cot2θ.Cot3θ.Cot4θ. Cot(90° - 4θ).Cot(90° - 3θ).Cot(90° - 2θ).Cot(90° - θ).Cot90°

⇒ Cotθ.Cot2θ.Cot3θ.Cot4θ. tan 4θ. tan 3θ. tan 2θ. tan θ.1 = 1 (∵ tanθ = 1/cotθ)

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