If ( + 30^ ) = 3 12 , then find co s^2 ?

Answer: Option B

$$\begin{array}{rl}& \sin \left(\theta +{30}^{\circ }\right)=\frac{3}{\sqrt{12}}=\frac{3}{2\sqrt{3}}\\ & =\frac{\sqrt{3}}{2}=\sin \left(\theta +{30}^{\circ }\right)=\sin 60^{\circ }\\ & \therefore \theta =30^{\circ }\\ & \text{co}{\text{s}}^2\theta =\text{co}{\text{s}}^{2}30^{\circ }\\ & ={\left(\frac{\sqrt{3}}{2}\right)}^2\\ & =\frac{3}{4}\end{array}$$