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3. Euler's Formula from cosh(t)
Given
cosh
(
t
)
=
e
t
+
e
−
t
2
=
1
+
t
2
2
!
+
t
4
4
!
+
t
6
6
!
+
⋯
\cosh(t) = \frac{e^t + e^{-t}}{2} = 1 + \frac{t^2}{2!} + \frac{t^4}{4!} + \frac{t^6}{6!} + \cdots
cosh
(
t
)
=
2
e
t
+
e
−
t
=
1
+
2
!
t
2
+
4
!
t
4
+
6
!
t
6
+
⋯
derive Euler's formula
e
i
x
=
cos
(
x
)
+
i
sin
(
x
)
.
e^{ix} = \cos(x) + i\sin(x).
e
i
x
=
cos
(
x
)
+
i
sin
(
x
)
.
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