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NDA 2021 Maths · Mathematics · Inverse Trigonometric Functions · easy

The value of cot (cos ^-18/17) is

Single correct option

The value of cot⁡(cos⁡−1817)\cot\left(\cos^{-1}\dfrac8{17}\right) is
  1. A. 158\dfrac{15}8
  2. B. 815\dfrac8{15}
  3. C. 817\dfrac8{17}
  4. D. 1715\dfrac{17}{15}
Show answer and solution

Answer: (B) 815\dfrac8{15}

Let cos⁡θ=817\cos\theta=\tfrac8{17} with θ\theta acute. Then sin⁡θ=1517\sin\theta=\tfrac{15}{17} (8-15-17 triangle) and cot⁡θ=cos⁡θsin⁡θ=815\cot\theta=\tfrac{\cos\theta}{\sin\theta}=\tfrac8{15}. The reciprocal 158\tfrac{15}8 is tan⁡θ\tan\theta.
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Original question written in the NDA 2021 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake