frac{d^2}{dx^2}(2cos x cos 3x) = | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given $y = 2\cos x \cos 3x$. Using the trigonometric identity $2\cos A \cos B = \cos(A+B) + \cos(A-B)$,we have: $y = \cos(x+3x) + \cos(x-3x) = \co

Vedclass · Accepted Answer

$-2^2(\cos 2x + 2^2\cos 4x)$

Vedclass · Answer

(D) Given $y = 2\cos x \cos 3x$. Using the trigonometric identity $2\cos A \cos B = \cos(A+B) + \cos(A-B)$,we have: $y = \cos(x+3x) + \cos(x-3x) = \cos 4x + \cos 2x$. Now,differentiate with respect to $x$: $\frac{dy}{dx} = \frac{d}{dx}(\cos 4x + \cos 2x) = -4\sin 4x - 2\sin 2x$. Differentiate again with respect to $x$: $\frac{d^2y}{dx^2} = \frac{d}{dx}(-4\sin 4x - 2\sin 2x) = -16\cos 4x - 4\cos 2x$. Factoring out $-4$: $\frac{d^2y}{dx^2} = -4(\cos 2x + 4\cos 4x) = -2^2(\cos 2x + 2^2\cos 4x)$.

$\frac{d^2}{dx^2}(2\cos x \cos 3x) = $

Similar Questions

If $y=\tan ^{-1}\left(\frac{\sqrt{1+a^2 x^2}-1}{a x}\right)$, then $\left(1+a^2 x^2\right)y''+2 a^2 x y'$ is equal to

If $y=e^{4x} \cos 5x$,then $\frac{d^{2}y}{dx^{2}}$ at $x=0$ is

If $(a+bx) e^{\frac{y}{x}}=x$,then $x^3 \frac{d^2 y}{d x^2}$ is equal to

If $f(x) = a\sin (\log x)$,then ${x^2}f''(x) + xf'(x) = . . . $

If $y=A \sin x+B \cos x$,then prove that $\frac{d^{2} y}{d x^{2}}+y=0$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module