Question

The general solution of the equation $\sin x+\cos x=\frac{3}{2}$ is

• A. $n\pi +\frac{\pi }{6},n\in Z$
• B. $2n\pi +\frac{\pi }{3},n\in Z$
• C. $n\pi +\frac{\pi }{3},n\in Z$
• D. no solution

Answer 1

The correct option is D no solution

$\frac{1}{\sqrt{2}}\sin x+\frac{1}{\sqrt{2}}\cos x=\frac{3}{2\sqrt{2}}$
$\sin (x+\frac{\pi }{4})=\frac{3}{2\sqrt{2}}>1$
so there is no solution.