If + = /2 and = 1/2, then the value of sin is?

Answer: Option D

$$\begin{array}{rl}& \theta +\varphi =\frac{\pi }{2}\\ & \theta +\varphi =90^{\circ }......(i)\\ & \sin \theta =\frac{1}{2}\\ & \sin \theta =\text{sin 3}{0}^{\circ }=\frac{1}{2}......(ii)\\ & \text{Put }\theta =30^{\circ }\text{ in equation (i)}\\ & 30^{\circ }+\varphi =90^{\circ }\\ & \varphi =60^{\circ }\\ & \sin \varphi =\sin 60^{\circ }=\frac{\sqrt{3}}{2}\end{array}$$