求证:sin(x-y)sin(x+y)/sin²xcos²y=1-cot²xtan²y
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求证:sin(x-y)sin(x+y)/sin²xcos²y=1-cot²xtan²y
求证:sin(x-y)sin(x+y)/sin²xcos²y=1-cot²xtan²y
求证:sin(x-y)sin(x+y)/sin²xcos²y=1-cot²xtan²y
sin(x-y)=sinxcosy-cosxsiny,
sin(x+y)=sinxcosy+cosxsiny
sin(x-y)sin(x+y)=sin²xcos²y-cos²xsin²y
sin(x-y)sin(x+y)/sin²xcos²y=(sin²xcos²y-cos²xsin²y)/sin²xcos²y
=1-cot²xtan²y
1.左边 分母乘过去
2.右边切化弦
3.右边用平方差公式
4.逆用2角和差正弦公式
可选
3 左边2交正弦和差公式打开 和右边一样
由于sin(x-y)=sinxcosy-cosxsiny,sin(x+y)=sinxcosy+cosxsiny
所以sin(x-y)sin(x+y)=sin²xcos²y-cos²xsin²y
所以左式=1-cos²xsin²y/sin²xcos²y=1-cot²xtan²y
证毕
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