已知sin(x+y)=1/2,sin(x-y)=1/3,求tanx,tany
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已知sin(x+y)=1/2,sin(x-y)=1/3,求tanx,tany
要不然我是看不懂的
要不然我是看不懂的
sin(x+y)=1/2,则sinxcosy+cosxsiny = 1/2
sin(x-y)=1/3,则sinxcosy-cosxsiny = 1/3
解之可得 sinxcosy = 5/12
cosxsiny = 1/12
上式除以下式可得 tanx=5tany;且有:
cosy=5/(12sinx); siny=1/(12cosx);
利用cos^2y + sin^2y = 1,代入可得:
25/(144sin^2x) + 1/(144cos^2x) = 1
则两边同乘以144cos^2x,可得:
25/(tan^2x) + 1 = 144/(1+tan^2x)
其中1/cos^2x=sec^2x=1+tan^2x
化简上式可得:tan^4x - 118tan^2x + 25 = 0
解之可得 tan^2x = 117.79 或 tan^2x = 0.212;
则tanx = 正负 10.85 或 tanx = 正负 0.461;
利用tanx=5tany对应的tany:
则tany = 正负 2.171 或 tanx = 正负 0.0922;
sin(x-y)=1/3,则sinxcosy-cosxsiny = 1/3
解之可得 sinxcosy = 5/12
cosxsiny = 1/12
上式除以下式可得 tanx=5tany;且有:
cosy=5/(12sinx); siny=1/(12cosx);
利用cos^2y + sin^2y = 1,代入可得:
25/(144sin^2x) + 1/(144cos^2x) = 1
则两边同乘以144cos^2x,可得:
25/(tan^2x) + 1 = 144/(1+tan^2x)
其中1/cos^2x=sec^2x=1+tan^2x
化简上式可得:tan^4x - 118tan^2x + 25 = 0
解之可得 tan^2x = 117.79 或 tan^2x = 0.212;
则tanx = 正负 10.85 或 tanx = 正负 0.461;
利用tanx=5tany对应的tany:
则tany = 正负 2.171 或 tanx = 正负 0.0922;
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