Q.

The number of real roots of the equation esin⁡x−e−sin⁡x−4=0 are

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a

1

b

2

c

Infinite

d

None of these

answer is D.

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Detailed Solution

. Given equation is esin⁡x−e−sin⁡x−4=0Let esin⁡x=y,then given equation can be written asy2−4y−1=0⇒y=2±5But the value ofy=esin⁡x' is always positive, so we take only y=2+5⇒loge⁡y=loge⁡(2+5)⇒sin⁡x=loge⁡(2+5)>1Which is impossible since sin x  cannot be greaterthan 1.Hence, we cannot find any real value of x which satisfiesthe given equation.
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The number of real roots of the equation esin⁡x−e−sin⁡x−4=0 are