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NDA 2024 Maths · Mathematics · Inverse Trigonometric Functions · medium

If θ=cos ^-17/25, then cot θ equals

Single correct option

If θ=cos⁡−1725\theta=\cos^{-1}\dfrac7{25}, then cot⁡θ\cot\theta equals
  1. A. 247\dfrac{24}{7}
  2. B. 724\dfrac7{24}
  3. C. 725\dfrac{7}{25}
  4. D. 2425\dfrac{24}{25}
Show answer and solution

Answer: (B) 724\dfrac7{24}

cos⁡θ=725\cos\theta=\frac7{25}, θ∈[0,π]\theta\in[0,\pi] so sin⁡θ=2425\sin\theta=\frac{24}{25}. Then cot⁡θ=cos⁡θsin⁡θ=724\cot\theta=\frac{\cos\theta}{\sin\theta}=\frac7{24}. Trap: inverting gives tan⁡θ=247\tan\theta=\frac{24}7.
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