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NDA 2023 Maths · Mathematics · Inverse Trigonometric Functions · medium

The value of tan (sin ^-15/13) is

Single correct option

The value of tan⁡(sin⁡−1513)\tan\left(\sin^{-1}\dfrac5{13}\right) is
  1. A. 513\dfrac5{13}
  2. B. 1213\dfrac{12}{13}
  3. C. 125\dfrac{12}{5}
  4. D. 512\dfrac5{12}
Show answer and solution

Answer: (D) 512\dfrac5{12}

Let θ=sin⁡−1513\theta=\sin^{-1}\frac5{13}, an acute angle with sin⁡θ=513\sin\theta=\frac5{13}. Then cos⁡θ=1213\cos\theta=\frac{12}{13} and tan⁡θ=512\tan\theta=\frac{5}{12}. Writing 125\frac{12}5 inverts the ratio, and 513\frac5{13} is just sin⁡θ\sin\theta.
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Original question written in the NDA 2023 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