Find the limit
lim
x
→
π
2
sin
(
x
−
π
2
)
x
−
π
2
=
\displaystyle \lim_{{{x}\rightarrow\frac{\pi}{{2}}}}{\frac{{{\sin{{\left({x}-\frac{\pi}{{2}}\right)}}}}}{{{x}-\frac{\pi}{{2}}}}}=
x
→
2
π
lim
x
−
2
π
sin
(
x
−
2
π
)
=
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