Question

If $\sqrt{2}\sin ({60}^{\circ }-\alpha )=1$, then the value of $\alpha$ is:

• A. ${45}^{\circ }$
• B. ${15}^{\circ }$
• C. ${60}^{\circ }$
• D. ${30}^{\circ }$

Answer 1

Answer: (B)

${15}^{\circ }$

$\sqrt{2}\sin ({60}^{\circ }-\alpha )=1$

$\Rightarrow \sin ({60}^{\circ }-\alpha )=\frac{1}{\sqrt{2}}$

$\Rightarrow \sin ({60}^{\circ }-\alpha )=\sin {45}^{\circ }$

$\Rightarrow ({60}^{\circ }-\alpha )={45}^{\circ }$

$\Rightarrow \alpha ={60}^{\circ }-{45}^{\circ }$

$\Rightarrow \alpha ={15}^{\circ }$

Hence, value of $\alpha$ is equal to ${15}^{\circ }.$