A) \[y=\sin x+\text{cosec }x\]
B) \[y=\tan \frac{x}{2}+\cot \frac{x}{2}\]
C) \[y=\frac{1}{\sqrt{2}}\sec \frac{x}{2}+\sqrt{2}\cos \frac{x}{2}\]
D) None of these
Correct Answer: A
Solution :
\[\frac{dy}{dx}=2\cos x-y\cot x\] Þ \[\frac{dy}{dx}+y\cot x=2\cos x\] I.F.\[={{e}^{\int{\cot xdx}}}=\sin x\] \[y.\sin x=\int{2\cos x.\sin x+c}\] \[y\sin x={{\sin }^{2}}x+c\] at \[y=2\] and \[x=\frac{\pi }{2}\], \[c=1\]; \[y=\sin x+\cos \text{ec}x\]
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