y = \(\cfrac12\) [sin(5x + 3x) + sin(5x - 3x)]
y = \(\cfrac12\) sin 8x + \(\cfrac12\) sin 2x
Differentiating with respect to x
\(\cfrac{dy}{d\text x}
\) = \(\cfrac82\) cos 8x + \(\cfrac22\) cos 2x
⇒ \(\cfrac{dy}{d\text x}
\) = 4 cos 8x + cos 2x
Differentiating with respect to x
\(\cfrac{d^2y}{d\text x^2}
\) = -32 sin 8x - 2 sin 2x
Hence Proved