已知函数f(x)=2√3sin(x+π/4)•cos(x+π/4)-sin(2x+3π)(1)求f
已知函数f(x)=2√3sin(x+π/4)•cos(x+π/4)-sin(2x+3π)(1)求f(x)的最小正周期...
已知函数f(x)=2√3sin(x+π/4)•cos(x+π/4)-sin(2x+3π)(1)求f(x)的最小正周期
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解：
f(x)
=2√3sin(x+π/4)•cos(x+π/4)-sin(2x+3π)
=√3sin(2x+π/2)-[-sin(2x)]
=√3cos(2x)+sin(2x)
=2[sin(π/3)cos(2x)+cos(π/3)sin(2x)]
=2sin(2x+π/3)
最小正周期是：
2π/2=π
f(x)
=2√3sin(x+π/4)•cos(x+π/4)-sin(2x+3π)
=√3sin(2x+π/2)-[-sin(2x)]
=√3cos(2x)+sin(2x)
=2[sin(π/3)cos(2x)+cos(π/3)sin(2x)]
=2sin(2x+π/3)
最小正周期是：
2π/2=π
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