# Find the integration of:

\int_{-\pi}^{\pi}\frac{sin2x}{sinx}dx=?

step by step solution:

Recall the Double-Angle Identity:

For an angle x , the double-angle identity for sine is:

sin2x=2sinxcosx

Using this formula we can write

\int_{-\pi}^{\pi} \frac{\textcolor{primary}{2\sin{x}\cdot \cos{x}}}{\sin{x}}~dx

By simplifying the above integral we get

\int_{-\pi}^{\pi} (\textcolor{primary}{2\cos{x)}}~dx \implies0

The required value of the given integral is:

\int_{-\pi}^{\pi} \frac{\sin2x}{\sin{x}}=0

You may like:

1. Find The rate at which the observer’s head is tilting when the angle of inclination is 60 degrees: