1.

If cosec θ + cot θ = 5/2, then the value of tan θ is(A) 14/15(B) 20/21(C) 21/20(D) 15/16

Answer»

Correct option is (B) 20/21

cosec θ + cot θ = 5/2……(i) 

cosec2 θ – cot2 θ = 1

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

 ∴ 5/2 (cosec θ – cot θ) = 1

∴ cosec θ – cot θ = 2/5...(ii)

Subtracting (ii) from (i), we get

2 cot θ = 5/2 - 2/5 = 21/10

∴ cot θ = 21/20

∴ tan θ = 20/21



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