Given that $\sin \alpha=\frac{\sqrt{3}}{2}$ and $ an \beta=\frac{1}{\sqrt{3}}$, then the value of $

Question

Given that $\sin \alpha=\frac{\sqrt{3}}{2}$ and $	an \beta=\frac{1}{\sqrt{3}}$, then the value of $\cos (\alpha-\beta)$ is\

Professor PC Thomas Classes · Answer

(a):Given, $\sin \alpha=\frac{\sqrt{3}}{2}$\ $\Rightarrow \alpha=60^{\circ}$ $$ \left(\because \quad \sin 60^{\circ}=\frac{\sqrt{3}}{2}ight) $$ and $	an \beta=\frac{1}{\sqrt{3}}$\ $\Rightarrow \beta=30^{\circ}$ $$ \left(\because \quad 	an 30^{\circ}=\frac{1}{\sqrt{3}}ight) $$ Now, $\cos (\alpha-\beta)=\cos \left(60^{\circ}-30^{\circ}ight)=\cos 30^{\circ}=\frac{\sqrt{3}}{2}$\