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TS EAMCET · Maths · Differentiation

If \(y=a \cos (\sin 2 x)+b \sin (\sin 2 x)\), then \(y^{\prime \prime}+(2 \tan 2 x) y^{\prime}\) is equal to

  1. A 0
  2. B \(4\left(\cos ^2 2 x\right) y\)
  3. C \(-4\left(\cos ^2 2 x\right) y\)
  4. D \(-\left(\cos ^2 2 x\right) y\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(-4\left(\cos ^2 2 x\right) y\)

Step-by-step Solution

Detailed explanation

Given, \[ y=a \cos (\sin 2 x)+b \sin (\sin 2 x) \] On differentiating both sides w.r.t. \(x\), we get \[ \begin{aligned} y^{\prime}=-a & \sin (\sin 2 x) \cos 2 x \cdot 2 \\ & +b \cos (\sin 2 x) \cdot(\cos 2 x) \cdot 2 \end{aligned} \]…