$\cos 1^\circ + \cos 2^\circ + \cos 3^\circ + ..... + \cos 180^\circ = $
$0$
$1$
$-1$
$2$
Prove that: $(\sin 3 x+\sin x) \sin x+(\cos 3 x-\cos x) \cos x=0$
Find the angle in radian through which a pendulum swings if its length is $75\, cm$ and the tip describes an arc of length.
$15\,cm$
In a right angled triangle the hypotenuse is $2 \sqrt 2$ times the perpendicular drawn from the opposite vertex. Then the other acute angles of the triangle are
Prove that $\cos \left(\frac{3 \pi}{4}+x\right)-\cos \left(\frac{3 \pi}{4}-x\right)=-\sqrt{2} \sin x$
Find the value of $\sin \frac{31 \pi}{3}$.