JEE Mains · Maths · STD 12 - 5. continuity and differentiation
If \(y = \tan^{-1}\left(\dfrac{3\cos x - 4\sin x}{4\cos x + 3\sin x}\right) + 2\tan^{-1}\left(\dfrac{x}{1+\sqrt{1-x^2}}\right)\), then \(\dfrac{dy}{dx}\) at \(x = \dfrac{\sqrt{3}}{2}\) is equal to:
- A \(3\)
- B \(-1\)
- C \(1\)
- D \(2\)
Answer & Solution
Correct Answer
(C) \(1\)
Step-by-step Solution
Detailed explanation
Let \(y = y_1 + y_2\) \(y_1 = \tan^{-1}\left(\dfrac{3\cos x - 4\sin x}{4\cos x + 3\sin x}\right)\) Dividing the numerator and denominator by \(4\cos x\): \(y_1 = \tan^{-1}\left(\dfrac{\dfrac{3}{4} - \tan x}{1 + \dfrac{3}{4}\tan x}\right)\) Using the formula…
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