根号[1-2sin(3-π)cos(3-π)]化简

根号[1-2sin(3-π)cos(3-π)]化简
根号[1-2sin(3-π)cos(3-π)]化简

根号[1-2sin(3-π)cos(3-π)]化简
√[1-2sin(3-π)cos(3-π)]
=√[sin²(3-π)+cos²(3-π)-2sin(3-π)cos(3-π)]
=√[sin(3-π)-cos(3-π)]²
=|sin(3-π)-cos(3-π)|
=|-sin(π-3)-cos(π-3)|
因为π-3=0.141……是第一象限角,
所以原式=sin(π-3)+cos(π-3)=sin3-cos3.
也可以从头一步就用诱导公式.
化为|sin3-cos3|.
因为3是第二象限角,所以sin3>0,cos3