If $\mathrm{y}=\cos ^{2}\left(\frac{5 x}{2}\right)-\sin ^{2}\left(\frac{5 x}{2}\right)$, then…
If $\mathrm{y}=\cos ^{2}\left(\frac{5 x}{2}\right)-\sin ^{2}\left(\frac{5 x}{2}\right)$, then $\left(\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{d} x^{2}}\right)=$
$-5 \sqrt{1-y^{2}}$
$5 \sqrt{1-y^{2}}$
$25 y$
$-25 y$
Solution
Given
$\begin{aligned}
y &=\cos ^{2}\left(\frac{5 x}{2}\right)-\sin ^{2}\left(\frac{5 x}{2}\right) \\
y &=\cos \left(2 \times \frac{5 x}{2}\right) \Rightarrow y=\cos 5 x \\
\therefore \frac{d y}{d x} &=-5 \sin 5 x \Rightarrow \frac{d^{2} y}{d x^{2}} \\
&=-25 \cos 5 x=-25 y
\end{aligned}$