Question

Solve $\sqrt{2}\left(\sin x+\cos x\right)=\sqrt{3}$

Answer 1

$\sqrt{2}(\sin x+\cos x)=\sqrt{3}$

${(\sin x+\cos x)}^2={\left(\frac{\sqrt{3}}{\sqrt{2}}\right)}^2$

${\sin }^{2}x+{\cos }^{2}x+2\sin x\cos x=\frac{3}{2}$

$2\sin x\cos x=\frac{1}{2}$

$\sin 2x=\frac{1}{2}$$2x=30$ or $150$

$x=15$ or $75$