The number of solutions, of the equation math | vedclass

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Question

Take $e^{\sin x}=t(t>0)$

$\Rightarrow \mathrm{t}-\frac{2}{\mathrm{t}}=2$

$\Rightarrow \frac{\mathrm{t}^2-2}{\mathrm{t}}=2$

$\Rightarrow \m

Vedclass · Accepted Answer

$0$

Vedclass · Answer

Take $e^{\sin x}=t(t>0)$

$\Rightarrow \mathrm{t}-\frac{2}{\mathrm{t}}=2$

$\Rightarrow \frac{\mathrm{t}^2-2}{\mathrm{t}}=2$

$\Rightarrow \mathrm{t}^2-2 \mathrm{t}-2=0$

$\Rightarrow \mathrm{t}^2-2 \mathrm{t}+1=3$

$\Rightarrow(\mathrm{t}-1)^2=3$

$\Rightarrow \mathrm{t}=1 \pm \sqrt{3}$

$\Rightarrow \mathrm{t}=1 \pm 1.73$

$\Rightarrow \mathrm{t}=2.73 	ext { or }-0.73(	ext { rejected as } \mathrm{t}>0)$

$\Rightarrow \mathrm{e}^{\sin \mathrm{x}}=2.73$

$\Rightarrow \log _{\mathrm{e}} \mathrm{e}^{\sin \mathrm{x}}=\log _{\mathrm{e}} 2.73$

$\Rightarrow \sin \mathrm{x}=\log _{\mathrm{e}} 2.73>1$

So no solution.

The number of solutions, of the equation $\mathrm{e}^{\sin x}-2 e^{-\sin x}=2$ is

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