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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

NDA 2022 · Mathematics · Inverse Trigonometric Functions

If 3 ^ -1 x+ ^ -1 x=π , then what is x equal to?

If 3sin⁡−1x+cos⁡−1x=π3 \sin ^{-1} x+\cos ^{-1} x=\pi, then what is xx equal to?

Options

  1. A0
  2. B12\frac{1}{2}
  3. C12\frac{1}{\sqrt{2}}
  4. D13\frac{1}{\sqrt{3}}

Correct answer

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

Step-by-step solution

3sin⁡−1x+cos⁡−1x=π⇒2sin⁡−1x+sin⁡−1x+cos⁡−1x=π\begin{aligned} & 3 \sin ^{-1} x+\cos ^{-1} x=\pi \\ \Rightarrow \quad & 2 \sin ^{-1} x+\sin ^{-1} x+\cos ^{-1} x=\pi\end{aligned}⇒2sin⁡−1x+π2=π⇒2sin⁡−1x=π2⇒sin⁡−1x=π4⇒x=sin⁡π4=12\begin{aligned} & \Rightarrow \quad 2 \sin ^{-1} x+\frac{\pi}{2}=\pi \\ & \Rightarrow \quad 2 \sin ^{-1} x=\frac{\pi}{2} \quad \Rightarrow \quad \sin ^{-1} x=\frac{\pi}{4} \\ & \Rightarrow \quad x=\sin \frac{\pi}{4}=\frac{1}{\sqrt{2}}\end{aligned}$
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