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Q.
If $x\,sin\left(a+y\right)=siny$, then $\frac{dy}{dx}$ is equal to
Continuity and Differentiability
Solution:
Given $x\,sin\left(a+y\right)=siny$
$\Rightarrow x=\frac{sin\,y}{si n\left(a+y\right)}$
Differentiate both sides $w$.$r$.$t$. $x$, we get
$1=\frac{sin\left(a+y\right)cos\,y \frac{dy}{dx}-cos\left(a+y\right)sin\,y \frac{dy}{dx}}{sin^{2}\left(a+y\right)}$
$\Rightarrow sin^{2}\left(a+y\right)=sin\left(a+y-y\right) \frac{dy}{dx}$
$\Rightarrow \frac{dy}{dx}=\frac{sin^{2}\left(a+y\right)}{sin\,a}$