If esinx−e−sinx−4=0,then,x=
none of these
Given equation:esinx−e−sinx−4=0Let:esinx=yNow,y−y−1−4=0⇒y2−4y−1=0∴y=4±√16+42⇒y=4±√202⇒y=4±√52=2±√5And,y=esin x⇒esin x=2±√5Taking log on both sides,we get:sin x=loge(2±√5)⇒sin x=sin x=loge(2±√5)or sin x =loge(2−√5)⇒sin x=loge(4.24)or sin x=loge(−0.24)loge(4.24)>1 and sin x cannot be greater than 1.in the other case, the log of negative term occurs, which is not defined.