Question

( e^{sin 1}-e^{-sin x}-4=0 )
tet ( y=e^{sin n} )
( y-frac{1}{y}-4=0 )
( y^{2}-4 y-1=0 )
( y=2+sqrt{5} s^{2-sqrt{5}} )
since ( y ) is real
( y eq 2-sqrt{5} )
( e^{sin n}=2+sqrt{5} )
( sin n=log _{e}(2+sqrt{5}) )
( 21 sqrt{5}>e Rightarrow log _{e}(2+sqrt{5})>log _{e} e )
reat po ( log _{e}(2+sqrt{5})>1 )
tence ( sin x>1[text { not poset }] 4 )
no real solution

# [AIEEE he equation esinx - e-sin x - 4 = 0 has 1) exactly one real root. ) infinite number of real roots. (B) exactly four real root. (D) no real roots. [30104

Solution