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$e^{\sin x} - e^{- \sin x} = 4$ for

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all real values of x

some x ∈[0, π/2]

some x∈(−π/2, π/2)

no real value of x

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detailed solution

Correct option is D

esin⁡x=4+1esin⁡x−1≤sin⁡x≤1 and e>1e−1≤esin⁡x≤e<3.⇒esin⁡x<3, also esin⁡x>0.∴1esin⁡x+4>4.So two sides of (1) cannot be equal for any real value of x.

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esin⁡ x−e−sin⁡ x=4 for

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$e^{\sin x} - e^{- \sin x} = 4$ for