The value of \( \int \frac{(\cos 2 x)^{2}}{\sin x} d x \) (a) \[ \begin{array}{l} -\ln \left[\co...

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The value of \( \int \frac{(\cos 2 x)^{2}}{\sin x} d x \)
(a)
\[
\begin{array}{l}
-\ln \left[\cot x+\sqrt{\cot ^{2} x-1}\right] \\
+\frac{1}{\sqrt{2}} \ln \left(\frac{\sqrt{2}+\sqrt{1-\tan ^{2} x}}{\sqrt{2}-\sqrt{1-\tan ^{2} x}}\right)+C
\end{array}
\]
(b)
\[
\begin{array}{l}
-\ln \left[\cot x+\sqrt{\cot ^{2} x-1}\right] \\
+\frac{1}{2} \ln \left(\frac{\sqrt{2}+\sqrt{1-\tan ^{2} x}}{\sqrt{2}-\sqrt{1-\tan ^{2} x}}\right)+C
\end{array}
\]
(c)
\[
\begin{array}{l}
-\ln \left[\cot x+\sqrt{\cot ^{2} x-1}\right] \\
+\frac{1}{2 \sqrt{2}} \ln \left(\frac{\sqrt{2}+\sqrt{1-\tan ^{2} x}}{\sqrt{2}-\sqrt{1-\tan ^{2} x}}\right)+C
\end{array}
\]
(d) None of these
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