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The equation e^sinx -e^-sinx -4=0 has

Answers (1)

D Deependra Verma

Solution: we have , $e^ sin x- e^ -sin x-4=0$

Put , $e^ sin x=u$ $.......(1)$

$herefore$ The given equation becomes

$u^2-4u-1=0Rightarrow u=2pmsqrt5$

Either $e^ sin x=2+sqrt5$ $..........(2)$

or $e^ sin x=2-sqrt5$ $..........(3)$

$(2)$ and $(3)$ is impossible because $frac1eleq e^sin xleq e$

$herefore$ the given equation has no real solution.

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