Question

\( \sin^{-1}(x - 1) + \cos^{-1}(x - 3) + \tan^{-1}\!\left(\frac{x}{2 - x^2}\right) = \cos^{-1} k + \pi \), then the value of \( k \) is __________.

• A. \( 0 \)
• B. \( -\frac{1}{\sqrt{2}} \)
• C. \( 1 \)
• D. \( \frac{1}{\sqrt{2}} \)

Hint:

For inverse trigonometric questions, first check the domain restrictionsThey often give the required value of the variable directly.

Answer 1

The Correct Option is D