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NDA 2025 Maths · Mathematics · Inverse Trigonometric Functions · medium

If sin ^-1x+sin ^-1y=(π)/(2) and x=3/5, then y equals

Single correct option

If sin⁡−1x+sin⁡−1y=π2\sin^{-1}x+\sin^{-1}y=\dfrac\pi2 and x=35x=\dfrac35, then yy equals
  1. A. 35\dfrac35
  2. B. 45\dfrac45
  3. C. 25\dfrac{2}{5}
  4. D. 15\dfrac{1}{5}
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Answer: (B) 45\dfrac45

From sin⁡−1y=π2−sin⁡−1x\sin^{-1}y=\frac\pi2-\sin^{-1}x we get y=sin⁡(π2−sin⁡−1x)=cos⁡(sin⁡−1x)=1−925=45y=\sin\left(\frac\pi2-\sin^{-1}x\right)=\cos\left(\sin^{-1}x\right)=\sqrt{1-\frac9{25}}=\frac45. The value 35\frac35 would hold only if sin⁡−1x\sin^{-1}x were π4\frac\pi4.
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