The number of real roots of the equation esinx−e−sinx−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 esinx−e−sinx−4=0Let esinx=y,then given equation can be written asy2−4y−1=0⇒y=2±5But the value ofy=esinx' is always positive, so we take only y=2+5⇒logey=loge(2+5)⇒sinx=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.