[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

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( 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

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