Question

If cosec θ + cot θ = 5/2, then the value of tan θ is

(A) \(\frac{14}{25}\)

(B) \(\frac{20}{21}\)

(C) \(\frac{21}{20}\)

(D) \(\frac{15}{16}\)

Answer 1

Correct answer is (B) \(\frac{20}{21}\)

Explanation :

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