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NDA 2010
Exam
NDA
Year
2010
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

NDA 2010 · Mathematics · Inverse Trigonometric Functions

If ^ -1 (5)/(x)+ ^ -1 (12)/(x)=(π)/(2) , then what is the value of...

If sin⁡−15x+sin⁡−112x=π2\sin ^{-1} \frac{5}{x}+\sin ^{-1} \frac{12}{x}=\frac{\pi}{2}, then what is the value of xx ?

Options

  1. A1
  2. B7
  3. C13
  4. D17

Correct answer

C. 13

Step-by-step solution

sin⁡−1π=π−sin⁡−112xsin⁡−1π=cos⁡−112x\begin{aligned} & \sin ^{-1} \pi=\pi-\sin ^{-1} \frac{12}{x} \\ & \sin ^{-1} \pi=\cos ^{-1} \frac{12}{x}\end{aligned} or cos⁡−1x2−25−x=cos⁡−112xor x−25−x=12xor x2=169⇒x=13\begin{aligned} & \text{ or } \cos ^{-1} \frac{\sqrt{x^2-25}}{-x}=\cos ^{-1} \frac{12}{x} \\ & \text{or } \frac{x-25}{-x}=\frac{12}{x} \\ & \text{or } x^2=169 \Rightarrow x=13\end{aligned}$
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