Question

Show that the equation e^sin x-e^-sin x-4=0 has no real root

Answer 1

esinx – e-sinx – 4 = 0

t = esinx

t – 1/t = 4

t2 – 4t – 1 = 0

t = 4 ± √16 + 4 / (2)

t = 4 ± 2√5 / (2)

t = 2 ± √5

esinx = 2 ± √5

-1 ≤ sinx ≤ 1

1/e ≤ esinx ≤ e