求解数学三角函数证明题
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求解数学三角函数证明题求解数学三角函数证明题求解数学三角函数证明题tg(a-c)/tga=[sin(a-c)cosa]/[cos(a-c)sina]所以[sin(a-c)cosa]/[cos(a-c)
求解数学三角函数证明题
求解数学三角函数证明题
求解数学三角函数证明题
tg(a-c)/tga=[sin(a-c)cosa]/[cos(a-c)sina]
所以[sin(a-c)cosa]/[cos(a-c)sina]+[sinbsinb]/[sinasina]=1
两边各乘以cos(a-c)sinasina,得到sin(a-c)sinacosa+sinbsinbcos(a-c)=cos(a-c)sinasina
sinacosa=(1/2)sin2a,sinasina=(1/2)-cos2a/2
所以sinbsinbcos(a-c)=(1/2)cos(a-c)-(1/2)cos(a-c)cos2a-(1/2)sin(a-c)sin2a
=(1/2)cos(a-c)-(1/2)[cos(a-c)cos2a+sin(a-c)sin2a]
=(1/2)cos(a-c)-(1/2)cos[2a-(a-c)]=(1/2)[cos(a-c)-cos(a+c)]=sinasinc
tgbtgb=sinbsinb/(1-sinbsinb)=sinasinc/(cosacosc)=tgatgc
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