Find the value

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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