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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 A No real roots
esinxesinx4=0
Let esinx=t
So, we get the following equation
t+1t=4
t24t1=0

t=(4)±424(1)(1)2=4±252
t=2+5 or 25
esinx= 2+5 and 25 is not possible.
Hence, no solution exists.

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