If $$\theta + \phi = \frac{\pi }{2}$$   and $$\sin \theta = \frac{1}{2},$$   then the value of $${\text{sin}}\phi $$  is?

Solution (By Examveda Team)

$$\eqalign{ & \theta + \phi = \frac{\pi }{2} \cr & \theta + \phi = {90^ \circ }\,......(i) \cr & \sin \theta = \frac{1}{2} \cr & \sin \theta = {\text{sin 3}}{0^ \circ } = \frac{1}{2}\,......(ii) \cr & {\text{Put }}\theta = {30^ \circ }{\text{ in equation (i)}} \cr & {30^ \circ } + \phi = {90^ \circ } \cr & \phi = {60^ \circ } \cr & \sin \phi = \sin {60^ \circ } = \frac{{\sqrt 3 }}{2} \cr} $$