Q178 / 270 · NDA 2023 (Phase 2) · Mathematics

What is $1+\sin ^2\left(\cos ^{-1}\left(\frac{3}{\sqrt{17}}\right)\right)$ equal to?

  • Correct answer
    A
    $\frac{25}{17}$
  • B
    $\frac{8}{17}$
  • C
    $\frac{9}{17}$
  • D
    $\frac{47}{17}$

Solution

$\begin{aligned} & \text { Given, } 1+\sin ^2\left(\cos ^{-1}\left(\frac{3}{\sqrt{17}}\right)\right) \\ & =1+1-\left(\cos \left(\cos ^{-1}\left(\frac{3}{\sqrt{17}}\right)\right)\right)^2 \\ & =2-\left(\frac{3}{\sqrt{17}}\right)^2=2-\frac{9}{17}=\frac{25}{17}\end{aligned}$

Hence, the correct answer is option: 'A'.

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