The number of solutions of the equation $4 e^{\sin x}-3 e^{-\sin x}+4=0$ in $[0,2 \pi]$ is

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Professor PC Thomas Classes · Answer

Let $y=e^{\sin x}$. $4y - 3/y + 4 = 0 \Rightarrow 4y^2 + 4y - 3 = 0 \Rightarrow (2y+3)(2y-1) = 0$. $y=1/2$. $\sin x = \ln(1/2) < 0$. 2 solutions in $[0,2\pi]$.