If e sin x- e -sin x- a -0 has no real solution- thenA- -a- -e2-1-e- -B- -a- -0- -C- -a- -e- -D- -a- -0- e-1-e

The correct option is A Let t = e^sinx⇒ t [ 1/e,e ] nbsp; Given equations reduces to t^2 at 1 = 0 nbsp; If parent equation has no solution , then deri ...

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Byju's Answer

Standard XII

Mathematics

Properties Derived from Trigonometric Identities

If e sin x- e...

Question

If $e^{s i n x} - e^{- s i n x} - a = 0$ has no real solution, then

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Solution

The correct option is A

Let t = $e^{s i n x} \Rightarrow t [\frac{1}{e}, e]$

Given equations reduces to $t^{2} - a t - 1 = 0$

If parent equation has no solution , then derived equation has no root $\in [\frac{1}{e}, e]$

For $t^{2} - a t - 1 = 0$ $0 = a^{2} + 4 > 0$ a $\in$ R also

If it has atleast one root in

= $(1e,0) then (e2−ae−1)(1e2−fracae−1)≤0$

= { $(e^{2} - 1) - a e} {(e^{2} - 1) + a e} \geq 0$

$\Rightarrow$ |a| $\leq \frac{e^{2} - 1}{e}$

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