1.

If cosec θ – cot θ = q, then the value of cot θ is(A) 2q/1+q2(B) 2q/1-q2(C) 1-q2/2q(D) 1+q2/2q

Answer»

Correct option is (C) 1-q2/2q 

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

2cot θ = 1/q - q

∴ cot θ = 1-q2/2q 



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