The number of solution of equation, $e^{c o s^{2} x} - e^{- c o s^{2} x} + 4 = 0$ in $[0, 2 π]$ is/are

1

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2

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3

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n o n e o f t h e s e

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Solution

The correct option is D $n o n e o f t h e s e$
$e^{c o s^{2} x} - e^{- c o s^{2} x} + 4 = 0$
suppose, $e^{c o s^{2} x} = y$
$\Rightarrow y - 1 / y + 4 = 0 \Rightarrow y^{2} + 4 y - 1 = 0$
$y = - 2 \pm \sqrt{5}$
but given, $0 \leq x \leq 2 π$
But, $0 \leq y \leq e$
Hence there is no solution in the given interval

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