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NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

NDA 2024 · Mathematics · Inverse Trigonometric Functions

If ^ -1 x= ^ -1 x , then which one of the following is correct?

If cos⁡−1x=sin⁡−1x\cos ^{-1} x=\sin ^{-1} x, then which one of the following is correct?

Options

  1. Ax=1x=1
  2. Bx=12x=\frac{1}{2}
  3. Cx=12x=\frac{1}{\sqrt{2}}
  4. Dx=13x=\frac{1}{\sqrt{3}}

Correct answer

C. x=12x=\frac{1}{\sqrt{2}}

Step-by-step solution

cos⁡−1x=sin⁡−1x\cos ^{-1} x=\sin ^{-1} x⇒π2−sin⁡−1x=sin⁡−1x⇒2sin⁡−1x=π2⇒sin⁡−1x\begin{aligned} & \Rightarrow & \frac{\pi}{2}-\sin ^{-1} x & =\sin ^{-1} x \\ & \Rightarrow & 2 \sin ^{-1} x & =\frac{\pi}{2} \\ & \Rightarrow & & \sin ^{-1} x\end{aligned}$$
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