Question

For all $\theta$, the value of $\sin \theta +\sin (\theta +\pi )+\sin (2\pi +\theta )$ equals:

• A. $-\sin \theta$
• B. $\sin \theta$
• C. $2\sin \theta$
• D. $3\sin \theta$
• E. $2\sin \theta +\cos \theta$

Answer 1

The correct option is B $\sin \theta$

The value of $\sin \theta +\sin (\theta +\pi )+\sin (\theta +2\pi )$
We know, $\sin (\theta +\pi )=-\sin \theta$ and $\sin (2\pi +\theta )=\sin \theta$

$=\sin \theta -\sin \theta +\sin \theta$

$=\sin \theta$