Question

$\sin (\pi -\theta )+\cos (\frac{3\pi }{2}+\theta )+\sin (\pi +\theta )+\cos (\frac{3\pi }{2}-\theta )=?$

Answer 1

$\sin (\pi -\theta )+\cos (\frac{3\pi }{2}+\theta )+\sin (\pi +\theta )+\cos (\frac{3\pi }{2}-\theta )$

$\Rightarrow \sin \theta +\sin \theta -\sin \theta -\sin x$

$\Rightarrow 0$

$\left[\begin{array}{cc}\sin (\pi -\theta )=\sin \theta & \cos (\frac{3\pi }{2}+\theta )=\sin \theta \\ \sin (\pi +\theta )=-\sin \theta & \cos (\frac{3\pi }{2}-\theta )=-\sin \theta \end{array}\right]$.