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Mathematics
Mathematics
Problem
For all
x
x
x
such that
sin
x
>
0
\sin x>0
sin
x
>
0
, which of the following identities is correct? a)
(
sin
x
)
x
=
e
x
sin
x
(\sin x)^x = e^{x\sin x}
(
sin
x
)
x
=
e
x
s
i
n
x
b)
(
sin
x
)
x
=
e
(
ln
x
)
sin
x
(\sin x)^x = e^{(\ln x)\sin x}
(
sin
x
)
x
=
e
(
l
n
x
)
s
i
n
x
c)
(
sin
x
)
x
=
e
x
ln
(
sin
x
)
(\sin x)^x = e^{x\ln(\sin x)}
(
sin
x
)
x
=
e
x
l
n
(
s
i
n
x
)
d)
(
sin
x
)
x
=
e
ln
(
sin
x
x
)
(\sin x)^x = e^{\ln\left(\dfrac{\sin x}{x}\right)}
(
sin
x
)
x
=
e
l
n
(
x
sin
x
)
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