y=sin(5pai/6-x/2)cos(pai/6+x/2)单调减区间
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![y=sin(5pai/6-x/2)cos(pai/6+x/2)单调减区间](/uploads/image/z/12536777-65-7.jpg?t=y%3Dsin%285pai%2F6-x%2F2%29cos%28pai%2F6%2Bx%2F2%29%E5%8D%95%E8%B0%83%E5%87%8F%E5%8C%BA%E9%97%B4)
y=sin(5pai/6-x/2)cos(pai/6+x/2)单调减区间
y=sin(5pai/6-x/2)cos(pai/6+x/2)单调减区间
y=sin(5pai/6-x/2)cos(pai/6+x/2)单调减区间
y=sin(5π/6-x/2)cos(π/6+x/2)
=(sin5π/6cosx/2-cos5π/6sinx/2)(cosπ/6cosx/2-sinπ/6sinx/2)
=(1/2cosx/2+√3/2sinx/2)(√3/2cosx/2-1/2sinx/2)
=√3/4cos^2(x/2)-√1/4cosx/2sinx/2+3/4sinx/2cosx/2-√3/4sin^2(x/2)
=√3/4[cos^2(x/2)-sin^2(x/2)]+1/2sinx/2cosx/2
=1/4sinx+√3/4cosx
=1/2sin(x+π/3)
x+π/3=π/2+2kπ (k∈Z)
x=π/6+2kπ
x+π/3=3π/2+2kπ
x=7π/6+2kπ
单调递减区间为[π/6+2kπ,7π/6+2kπ](k∈Z)