Question

Solve: $\sin {690}^{\circ }\cos {930}^{\circ }+\tan (-{765}^{\circ })\text{cosec}(-{1170}^{\circ })$

Answer 1

$\sin 690°\cos 930°+\tan (-765°)\csc (-1170°)=\sin (720-30)\cos (900+30)+\tan (-720+45)\csc (3\times 360+90)=(-\sin 30°\left)\right(-\cos 30°)+\tan \left(45°\right)\csc \left(90°\right)=(-\frac{1}{2}\left)\right(-\frac{\sqrt{3}}{2})+(1\left)\right(1)=1+\frac{\sqrt{3}}{4}=\frac{\sqrt{3}+4}{4}$.