Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

$x=0$ is a root. Let $g(x)=\tan x-mx$. For $m>1,g^{\prime }(0)=1-m<0$, so $g<0$ just right of 0 , and $g\to \infty$ as $x\to {\frac{\pi }{2}}^{-}$. Hence there is one root in $\left(0,\frac{\pi }{2}\right)$ and, by symmetry, one in $\left(-\frac{\pi }{2},0\right)$. Total 3 roots.