已知sinx-cosx=根号2，x属于（0，TT),则tanx= 已知sinx+cosx=√2,x属于（0，派） 则tanx=...
\u5df2\u77e5sinx-cosx=\u6839\u53f72\uff0cx\u5c5e\u4e8e\uff080\uff0cTT),\u5219tanx=sinx-cosx=\u221a2
\u221a2sin(x-\u03c0/4)=\u221a2
sin(x-\u03c0/4)=1
\u6240\u4ee5
x-\u03c0/4=2k\u03c0+\u03c0/2
x=2k\u03c0+3\u03c0/4
x\u2208(0,\u03c0)
\u6240\u4ee5
0<2k\u03c0+3\u03c0/4<\u03c0
-3\u03c0/4<2k\u03c0<\u03c0/4
-3/8<k<1/8
\u6240\u4ee5 \u53ea\u80fd k=0
\u5f97 x=3\u03c0/4
\u6240\u4ee5 tanx=tan(3\u03c0/4)=-1
\u89e3\u51fa\uff1ax=pai/4
tanx=1
√2*(√2/2*sinx-√2/2*cosx)=√2
√2sin(x-π/4)=√2
x∈(0,π)
x-π/4∈(-π/4,3π/4)
当x-π/4=π/2时
即x=3π/4时，sinx-cosx=√2
tanx=tan3π/4=-1
因为sinx-cosx=根号2
由辅助角公式
2sin(x-π/4)=根号2
x=3π/4
tanx=-1
cos(a+b)=cosa*cosb-sina*sinb.
给方程两边同除以根号2
sin45*sinx-cos45*cosx=1=-cos（x+45）
然后自己看吧
由第一个等式可得X=（3/4）π，所以tanx=-1
-1
x=3π/4
-1
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