If y = cos^{2} frac{3x}{2} - sin^{2} frac{3x} | vedclass

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(C) Given,$y = \cos^{2} \frac{3x}{2} - \sin^{2} \frac{3x}{2}$.Using the trigonometric identity $\cos(2	heta) = \cos^{2}	heta - \sin^{2}	heta$,we ha

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$-9y$

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(C) Given,$y = \cos^{2} \frac{3x}{2} - \sin^{2} \frac{3x}{2}$.Using the trigonometric identity $\cos(2	heta) = \cos^{2}	heta - \sin^{2}	heta$,we have $	heta = \frac{3x}{2}$,so $2	heta = 3x$.Thus,$y = \cos(3x)$.Now,differentiate with respect to $x$:$\frac{dy}{dx} = -\sin(3x) \cdot 3 = -3\sin(3x)$.Now,differentiate again with respect to $x$:$\frac{d^{2}y}{dx^{2}} = -3 \cdot \cos(3x) \cdot 3 = -9\cos(3x)$.Since $y = \cos(3x)$,we substitute $y$ back into the expression:$\frac{d^{2}y}{dx^{2}} = -9y$.

If $y = \cos^{2} \frac{3x}{2} - \sin^{2} \frac{3x}{2}$,then $\frac{d^{2}y}{dx^{2}}$ is

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