A) \[\ell n\left( \sin \frac{x}{2} \right)+C\]
B) \[2\ell n\left( \cos \frac{x}{2} \right)+C\]
C) \[\ell n(1-\sin x)+C\]
D) \[\ell n(1-\cos x)+C\]
Correct Answer: D
Solution :
\[\int{\frac{\cos \text{ec}x+\cot x-(\cos \text{e}{{\text{c}}^{2}}x-{{\cot }^{2}}x)}{1+\cot x-\cos \text{ec}x}dx}\] \[=\int{(\cos ecx+\cot x)}dx\] \[=\ell n(\cos ecx-\cot x)+\ell \sin x+C\] \[=\ell n(1-\cos x)+C\]
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