1. Tardigrade
  2. Question
  3. Mathematics
  4. Solution set of the equation, cos -1 x- sin -1 x= cos -1(x √3)

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Solution set of the equation, $\cos ^{-1} x-\sin ^{-1} x=\cos ^{-1}(x \sqrt{3})$

Inverse Trigonometric Functions

Solution:

$\cos ^{-1} x+\sin ^{-1} x=\frac{\pi}{2} ;$ on subtraction, $2 \sin ^{-1} x=\frac{\pi}{2}-\cos ^{-1}(x \sqrt{3})=\sin ^{-1}(x \sqrt{3})$
$\Rightarrow 2 \alpha=\beta \Rightarrow 2 \sin \alpha \cos \alpha=\sin \beta \Rightarrow x=0, \pm 1 / 2$