1.

The integral \(\rm \int \sqrt {1 + 2 \cot x (cosec x + \cot x)} dx,\; \left( 0 < x < \frac \pi 2 \right)\) (where C is a constant of integration) is equal to

A. \(2 \log \left(\sin \frac x 2\right) + C\)
B. \(2 \log \left(\cos \frac x 2\right) + C\)
C. \(4 \log \left(\cos \frac x 2\right) + C\)
D. \(4 \log \left(\sin \frac x 2\right) + C\)
Answer» B. \(2 \log \left(\cos \frac x 2\right) + C\)


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