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JEE Main 2007
Exam
JEE Main
Year
2007
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

JEE Main 2007 · Mathematics · Inverse Trigonometric Functions

If ^ -1 ((x)/(5))+cosec^ -1 ((5)/(4))=(π)/(2) then a value of x is

If sin⁡−1\sin ^{-1}\left(\frac{x}{5}\right)+\operatorname{cosec}^{-1}(54)=π2\left(\frac{5}{4}\right)=\frac{\pi}{2} then a value of xx is

Options

  1. A11
  2. B33
  3. C44
  4. D55

Correct answer

B. 33

Step-by-step solution

sin⁡−1x5+sin⁡−145=π2\sin ^{-1} \frac{x}{5}+\sin ^{-1} \frac{4}{5}=\frac{\pi}{2} ⇒sin⁡−1x5=cos⁡−145⇒sin⁡−1x5=sin⁡−135\Rightarrow \sin ^{-1} \frac{x}{5}=\cos ^{-1} \frac{4}{5} \Rightarrow \sin ^{-1} \frac{x}{5}=\sin ^{-1} \frac{3}{5} ∴x=3\therefore x=3.
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