Question

Solve $\int \cot vdv$

• A. $\ln \sec v+C$
• B. $\ln \sin v+C$
• C. $\sin v+C$
• D. $\ln {\sec }^{2}v+C$

Answer 1

The correct option is B $\ln \sin v+C$

Consider, $I=\int \cot vdv$

$=\int \frac{\cos v}{\sin v}dv$

Let $\sin v=t$ $\Rightarrow \cos vdv=dt$ ( On differentiating w.r.t, v )

$\Rightarrow \int \frac{dt}{t}$

$=\log t+c=\log \sin v+c.$

Hence, the answer is $\log \sin v+c.$