ExamBro
ExamBro
TS EAMCET · Maths · Inverse Trigonometric Functions

If \(\sin ^{-1} x-\cos ^{-1} x=\frac{\pi}{6}\), then \(x\) is equal to

  1. A \(\frac{1}{2}\)
  2. B \(\frac{\sqrt{3}}{2}\)
  3. C \(-\frac{1}{2}\)
  4. D \(-\frac{\sqrt{3}}{2}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{\sqrt{3}}{2}\)

Step-by-step Solution

Detailed explanation

We have \(\sin ^{-1} x-\cos ^{-1} x=\frac{\pi}{6}\) Let \(A=\sin ^{-1} x\) \(\begin{array}{ll} \Rightarrow & x=\sin A, \cos A=\sqrt{1-x^2} \\ \text {and } & B=\cos ^{-1} x \\ \Rightarrow & x=\cos B, \sin B=\sqrt{1-x^2} \end{array}\) Now,…