作业帮证明sinx+cos(x+y)siny/cosx-sin(x+y)siny=tan(x+y)
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证明sinx+cos(x+y)siny/cosx-sin(x+y)siny=tan(x+y)
证明sinx+cos(x+y)siny/cosx-sin(x+y)siny=tan(x+y)
证明sinx+cos(x+y)siny/cosx-sin(x+y)siny=tan(x+y)
sin(x+y)=sinxcosy+cosxsiny 具体推导：首先建立直角坐标系,在直角坐标系cos(x+y) = cosx cosy - sinx siny sin(x+y) = sinx cosy + cosx
∵sinx=sin[﹙x＋y﹚-y]
=sin﹙x＋y﹚cosy-cos﹙x﹢y﹚siny
cosx=[﹙x＋y﹚-y]
=cos﹙x＋y﹚cosy＋sin﹙x﹢y﹚siny
∴原式＝[sin﹙x＋y﹚cosy-cos﹙x﹢y﹚siny+cos﹙x﹢y﹚siny]／[cos﹙x＋y﹚cosy＋sin﹙x﹢y﹚siny-sin﹙x﹢y﹚siny]
=[sin﹙...
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∵sinx=sin[﹙x＋y﹚-y]
=sin﹙x＋y﹚cosy-cos﹙x﹢y﹚siny
cosx=[﹙x＋y﹚-y]
=cos﹙x＋y﹚cosy＋sin﹙x﹢y﹚siny
∴原式＝[sin﹙x＋y﹚cosy-cos﹙x﹢y﹚siny+cos﹙x﹢y﹚siny]／[cos﹙x＋y﹚cosy＋sin﹙x﹢y﹚siny-sin﹙x﹢y﹚siny]
=[sin﹙x＋y﹚cosy]／[cos﹙x＋y﹚cosy]
=sin﹙x＋y﹚／cos﹙x＋y﹚=tan﹙x+y﹚
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