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in Trigonometry by (25.9k points)
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If cosec θ – cot θ = q, then the value of cot θ is

(A) \(\frac{2q}{1 + q^2}\)

(B) \(\frac{2q}{1 - q^2}\)

(C) \(\frac{1 - q^2}{2q}\)

(D) \(\frac{1 + q^2}{2q}\)

1 Answer

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Best answer

Correct answer is (C) \(\frac{1 - q^2}{2q}\)

Explanation :

cosec θ – cot θ = q ……(i) 

cosec2 θ – cot2 θ = 1 

∴ (cosec θ + cot θ) (cosec θ – cot θ) = 1 

∴ (cosec θ + cot θ)q = 1 

∴ cosec θ + cot θ = 1/q …….(ii) 

Subtracting (i) from (ii), we get

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