esin x−e−sin x=4 for
all real values of x
some x ∈[0, π/2]
some x∈(−π/2, π/2)
no real value of x
esinx=4+1esinx−1≤sinx≤1 and e>1e−1≤esinx≤e<3.⇒esinx<3, also esinx>0.∴1esinx+4>4.
So two sides of (1) cannot be equal for any real value of x.