证明tan(90°-y)=(2cos^3y-cosy)/(siny-2sin^3y)

来源：学生作业帮编辑：大师作文网作业帮分类：数学作业时间：2024/11/17 15:16:57

证明：∵tan(90°-y)=coty
=cosy/siny
=[cosy*cos(2y)]/[siny*cos(2y)]
=[cosy*(2cos²y-1)]/[siny*(1-2sin²y)] (应用余弦倍角公式)
=(2cos³y-cosy)/(siny-2sin³y)
∴原等式成立.
再问：噢这样啊如果不用cot可以吗因为我们没有学过
再答：就这样解吧：∵tan(90°-y)=sin(90°-y)/cos(90°-y) =cosy/siny =[cosy*cos(2y)]/[siny*cos(2y)] =[cosy*(2cos²y-1)]/[siny*(1-2sin²y)] (应用余弦倍角公式) =(2cos³y-cosy)/(siny-2sin³y) ∴原等式成立。

若cosx*cosy+sinx*siny=1/3 ,则cos(2x-2y)=? cosx+cosy=1/2,sinx-siny=1/3,则cos(x+y)=? 已知cosx+cosy=1/2,sinx-siny=1/3,求cos(x+y) 证明cosx(cosx-cosy)+sinx(sinx-siny)=2sin(x-y)/2 sinx+siny=-1/3 cosx+cosy=1/2,求sin(x+y)的值. 已知sinx+siny=1/3,cosx-cosy=1/5,求cos(x+y),sin(x-y). cos(2x+y)=3cosy,求tanx*tan(x+y) sinx+siny=1/3 ,cosx+cosy=1/2,求tan(x+y)的值．已知：3sinY=sin(2X+Y),求证tan(X+Y)=2tanX 已知5siny=sin(2x+y),求证:tan(x+y)=3/2tanx 若cos(x+y)cosy+sin(x+y)siny=0,则cosx= 已知cos(x+y)cosy+sin(x+y)siny=4/5,求tanx的值