Question

Want answer quickly
Solve for general values of theta: √3cos theta +sin theta =√2

Answer 1

$$\begin{gathered} \sqrt{3}\mathrm{cos\theta }+\mathrm{sin\theta }=\sqrt{2} \\ \mathrm{dividing}\mathrm{by}2,\mathrm{we}\mathrm{get} \\ \frac{\sqrt{3}}{2}\mathrm{cos\theta }+\frac{1}{2}\mathrm{sin\theta }=\frac{\sqrt{2}}{2}=\frac{1}{\sqrt{2}} \\ \sin \frac{\mathrm{\pi }}{3}\mathrm{cos\theta }+\cos \frac{\mathrm{\pi }}{3}\mathrm{sin\theta }=\sin \frac{\mathrm{\pi }}{4} \\ \sin \left(\frac{\mathrm{\pi }}{3}+\mathrm{\theta }\right)=\sin \frac{\mathrm{\pi }}{4} \\ \mathrm{General}\mathrm{solution}\mathrm{can}\mathrm{be}\mathrm{given}\mathrm{as}, \\ \frac{\mathrm{\pi }}{3}+\mathrm{\theta }=\mathrm{n\pi }+{\left(-1\right)}^{\mathrm{n}}\frac{\mathrm{\pi }}{4} \\ \mathrm{\theta }=\mathrm{n\pi }+{\left(-1\right)}^{\mathrm{n}}\frac{\mathrm{\pi }}{4}-\frac{\mathrm{\pi }}{3} \end{gathered}$$