Question

If $\sqrt{2}$ sin (60° – α) = 1 then α = ?
(a) 15°
(b) 30°
(c) 45°
(d) 60°

Answer 1

As we know that,
​$$\begin{gathered} \sin 45°=\frac{1}{\sqrt{2}} \\ \mathrm{Thus}, \\ \mathrm{if}\sqrt{2}\sin \left(60°-\alpha \right)=1 \\ \Rightarrow \sin \left(60°-\alpha \right)=\frac{1}{\sqrt{2}} \\ \Rightarrow 60°-\alpha =45° \\ \Rightarrow \alpha =60°-45° \\ \Rightarrow \alpha =15° \\ \mathrm{Hence},\mathrm{the}\mathrm{correct}\mathrm{option}\mathrm{is}\left(\mathrm{a}\right). \end{gathered}$$