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NDA 2020 Maths · Mathematics · Inverse Trigonometric Functions · hard

Tan (2cos ^-15/13) equals

Single correct option

tan⁡ ⁣(2cos⁡−1513)\tan\!\left(2\cos^{-1}\dfrac5{13}\right) equals
  1. A. 120119\dfrac{120}{119}
  2. B. 245\dfrac{24}{5}
  3. C. −119120-\dfrac{119}{120}
  4. D. −120119-\dfrac{120}{119}
Show answer and solution

Answer: (D) −120119-\dfrac{120}{119}

Let θ=cos⁡−1513\theta=\cos^{-1}\frac5{13}, so tan⁡θ=125\tan\theta=\frac{12}5. Then tan⁡2θ=2⋅1251−14425=24/5−119/25=−120119\tan2\theta=\dfrac{2\cdot\frac{12}5}{1-\frac{144}{25}}=\dfrac{24/5}{-119/25}=-\dfrac{120}{119}. Since 2θ>90∘2\theta>90^\circ, a negative value is expected.
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Original question written in the NDA 2020 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