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Question

The number of solution(s) of the equation esinxesinx4=0 is

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Solution

Given, esinxesinx4=0
Putting esinx=t, we get
t1t4=0t24t1=0t=4±202t=2±5esinx=2±5
As sinx[1,1]esinx[e1,e]
Now, we know that
2+5>e25<e1
So, the given equation has no solution.

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