A) \[\sin (a+y)\]
B) \[{{\sin }^{2}}(a+y)\]
C) \[\frac{{{\sin }^{2}}(a+y)}{\sin a}\]
D) \[\frac{\sin (a+y)}{\sin a}\]
E) \[\cos (a+y)\]
Correct Answer: C
Solution :
\[x=\frac{\sin y}{\sin (a+y)}\] On differentiating w.r.t. y, we get \[\frac{dx}{dy}=\frac{\sin (a+y)\cos y-\sin y\cos (a+y)}{{{\sin }^{2}}(a+y)}\] \[=\frac{\sin (a+y-y)}{{{\sin }^{2}}(a+y)}\] \[\Rightarrow \] \[\frac{dy}{dx}=\frac{{{\sin }^{2}}(a+y)}{\sin a}\]
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