A) \[{{\sin }^{2}}\,(a+y)/\sin a\]
B) \[\sin a/{{\sin }^{2}}\,(a+y)\]
C) \[\sin a/{{\sin }^{2}}\,(a-y)\]
D) \[{{\sin }^{2}}(a-y)\sin a\]
Correct Answer: A
Solution :
Given, \[\sin y=x\sin (a+y)\] \[\Rightarrow \] \[x=\frac{\sin y}{\sin (a+y)}\] On differentiating w. r. to x, we get \[1=\frac{\sin (a+y).cosy\frac{dy}{dx}-\sin y\cos (a+y)\frac{dy}{dx}}{{{\sin }^{2}}\,(a+y)}\] \[\Rightarrow \] \[1=\frac{\frac{dy}{dx}.\sin (a+y-y)}{{{\sin }^{2}}(a+y)}\] \[\Rightarrow \] \[\frac{dy}{dx}=\frac{{{\sin }^{2}}(a+y)}{\sin a}\]
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