Mathematics - Trigonometric Equation Question with Solution | TestHub

$[\sin x]=\frac{x}{2\pi }-\left[\frac{x}{2\pi }\right]+\frac{2x}{5\pi }-\left[\frac{2x}{5\pi }\right]$

The equation is $[sinx]=\{x/(2\pi )\}+\{2x/(5\pi )\}$. Since LHS is an integer and RHS is a sum of fractional parts, the only solution is when both sides are 0. This implies $sinx=0$, so $x=n\pi$. In $(30,40)$, $x=10\pi$ is the only solution.