Question

If y=sinx/1+cosx find dy/dx

Answer 1

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Answer 2

$y=\frac{sinx}{1+cosx}$

Using,

$sinx=2sin\frac{x}{2}cos\frac{x}{2}\\1+cosx=2cos^2\frac{x}{2}$

$y=\frac{2sin\frac{x}{2}cos\frac{x}{2}}{2sin^2\frac{x}{2}}\\y=\frac{sin\frac{x}{2}}{cos\frac{x}{2}}\\y=tan\frac{x}{2}$

Differentiate $y$ with respect to $x$,

$\frac{dy}{dx}=\frac{1}{2}sec^2\frac{x}{2}$