Question

If \( 2y = \left[ \cot^{-1} \left( \frac{\sqrt{3} \cos x + \sin x}{\cos x - \sqrt{3} \sin x} \right) \right]^2 \ \quad \forall x \in \left( 0, \frac{\pi}{2} \right), \text{ then } \frac{dy}{dx} \text{ is equal to:}\)}

• A. \( z - \frac{\pi}{4} \)
• B. \( 2x - \frac{\pi}{4} \)
• C. \( \frac{\pi}{4} - x \)
• D. \( \frac{\pi}{4} - x \)

Hint:

For differentiating inverse trigonometric functions, remember the standard identity: \[ \frac{d}{dx} \cot^{-1}(x) = -\frac{1}{1 + x^2}. \] Use the quotient rule for derivatives of rational functions.

Answer 1

The Correct Option is A