If + = 2; ( 0^ < 90^ ) , then sin\, ( 2 + 3 )^ is?

Answer: Option B

$$\begin{array}{rl}& \sin \alpha +\cos \beta =2\\ & \mathbf{Shortcut}\mathbf{method}:\\ & \text{Put, }\alpha =90^{\circ },\beta =0^{\circ }\\ & \iff \text{sin }90^{\circ }+\text{cos }{0}^{\circ }=2\\ & \iff 1+1=2\\ & \iff 2=2\left[\text{Matched}\right]\\ & \text{So, }\alpha =90^{\circ },\beta =0^{\circ }\\ & \Rightarrow \text{sin }{\left(\frac{2\alpha +\beta }{3}\right)}^{\circ }\\ & \Rightarrow \text{sin }{\left(\frac{2\times {90}^{\circ }+0^{\circ }}{3}\right)}^{\circ }\\ & \Rightarrow \text{sin }{\left(\frac{{180}^{\circ }}{3}\right)}^{\circ }\\ & \Rightarrow \text{sin }60^{\circ }=\cos 30^{\circ }=\frac{\sqrt{3}}{2}\\ & \text{Take cos}\frac{\alpha }{3}=\cos \frac{{90}^{\circ }}{3}\\ & =\text{cos 3}{0}^{\circ }\\ & \text{So, this is answer }\text{.}\end{array}$$