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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

NDA 2023 · Mathematics · Inverse Trigonometric Functions

What is 1+ ^2 ( ^ -1 ( 3 17 ))equal to?

What is 1+sin⁡2(cos⁡−1(317))equalto?1+\sin ^2 \left(\cos ^{-1} \left(\frac{3}{\sqrt{17}}\right)\right)equal to?

Options

  1. A2517\frac{25}{17}
  2. B817\frac{8}{17}
  3. C917\frac{9}{17}
  4. D4717\frac{47}{17}

Correct answer

A. 2517\frac{25}{17}

Step-by-step solution

 Given, 1+sin⁡2(cos⁡−1(317))=1+1−(cos⁡(cos⁡−1(317)))2=2−(317)2=2−917=2517\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}
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