Question:
$\mathrm{y}=\frac{1-\tan ^{2}(\mathrm{x} / 2)}{1+\tan ^{2}(\mathrm{x} / 2)}$, find $\frac{\mathrm{dy}}{\mathrm{dx}}$
Solution:
Formula:
Using Half angle formula,
$\cos x=\frac{1-\tan ^{2}(x / 2)}{1+\tan ^{2}(x / 2)}$
∴y = cos x
Differentiating y with respect to x
$\frac{d y}{d x}=\frac{d}{d x} \cos x$
$=-\sin x$
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