The correct option is B no real roots
Given equation isesinx−esinx−4=0
Put esin x=t in the given equation, we get
t2−4t−1=0
⇒t=4±√16+42=4±√202=4±2√52=2±√5
⇒esin x=2±√5(∴ t=esin x)
⇒esin x=2−√5 and esin x=2+√5
⇒esin x=2−√5<0 and sinx=ln(2+√5)>1
So rejected,
Hence given equation has no solution.
∴ The equation has no real roots.