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Question

The equation esinxesinx4=0 has:

A
infinite number of real roots
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B
no real roots
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C
exactly one real root
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D
exactly four real roots
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Solution

The correct option is B no real roots
Given equation isesinxesinx4=0
Put esin x=t in the given equation, we get
t24t1=0
t=4±16+42=4±202=4±252=2±5
esin x=2±5( t=esin x)
esin x=25 and esin x=2+5
esin x=25<0 and sinx=ln(2+5)>1
So rejected,
Hence given equation has no solution.
The equation has no real roots.

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