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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 |
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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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