ExamBro
ExamBro
AP EAMCET · Maths · Differentiation

If \(\mathrm{y}=(\mathrm{ax}+\mathrm{b}) \cos \mathrm{x}\), then \(\mathrm{y}_2+\mathrm{y}_1 \sin 2 \mathrm{x}+\mathrm{y}\left(1+\sin ^2 \mathrm{x}\right)=\)

  1. A \(y_2 \cos ^2 x\)
  2. B \(y_2 \sin ^2 x\)
  3. C \(y_1 \sin ^2 x\)
  4. D \(y \sin ^2 x\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(y_2 \sin ^2 x\)

Step-by-step Solution

Detailed explanation

\( y_1 = a\cos x - (ax+b)\sin x \) \( y_2 = -a\sin x - [a\sin x + (ax+b)\cos x] = -2a\sin x - (ax+b)\cos x \) \( y_2 = -2a\sin x - y \implies -2a\sin x = y_2+y \) \( y_2+y_1 \sin 2x+y(1+\sin ^2 x) = (-2a\sin x - y) + y_1 \sin 2x + y(1+\sin^2 x) \)…