PrepRung
Sign inSign up free

NDA 2016 Maths · Mathematics · Inverse Trigonometric Functions · hard

If sin ^-1x+sin ^-1y=(π)/(2), then x^2+y^2 is equal to

Single correct option

If sin⁡−1x+sin⁡−1y=π2\sin^{-1}x+\sin^{-1}y=\dfrac\pi2, then x2+y2x^2+y^2 is equal to
  1. A. 12\dfrac12
  2. B. 22
  3. C. 11
  4. D. 00
Show answer and solution

Answer: (C) 11

From sin⁡−1y=π2−sin⁡−1x\sin^{-1}y=\dfrac\pi2-\sin^{-1}x we get y=sin⁡(π2−sin⁡−1x)=cos⁡(sin⁡−1x)=1−x2y=\sin\left(\dfrac\pi2-\sin^{-1}x\right)=\cos(\sin^{-1}x)=\sqrt{1-x^2}. Squaring, y2=1−x2y^2=1-x^2, so x2+y2=1x^2+y^2=1. For example x=y=12x=y=\dfrac1{\sqrt2} satisfies the condition.
Report a mistake

Original question written in the NDA 2016 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake