I have one doubt. sinx/n=6. how?????
plzz answer my question correctly
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hence proved
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Answer:
- ni (ln √71 ) ± nπ/4
Step-by-step explanation:
sinx/n = 6
it is known that the sine function is governed by this inequality
-1 ≤ sinx ≤ 1
in the domain of real numbers
but we can find a solution in the domain of complex numbers
so far ;
let x/n = y , sin x/n = sin y = 6
sin y = 6 = (e^iy - e^-iy)/2i , i is the immaginery unit = √-1
e^iy - e^-iy = 12i , let e^iy = k
k - 1/k = 12i
k² - 12ik -1 = 0
k = (12i ± √-140)/2 = 6i ±√35 i ≈ √71 e∧±iπ/4 = e∧iy
iy = (ln √71 ) ± iπ/4 = ix/n
ix = n (ln √71 ) ± inπ/4
x = - ni (ln √71 ) ± nπ/4
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