方程cosx+sinx=cos2x的解集是?

熱心網(wǎng)友

cosx+sinx=cos2x---cosx+sinx=(cosx)^2-(sinx)^2---(cosx+sinx)(cosx-sinx)-(cosx+sinx)=0---(cosx+sinx)(cosx-sinx-1)=0---cosx+sinx=0orcosx-sinx=1cosx+sinx=0---sinx=-cosx---tanx=-1---x=kPi-Pi/4.(k是整數(shù))cosx-sinx=1---cosx*cos(Pi/4)-sinx*sin(Pi/4)=(2^.5)/2---cos(x+Pi/4)=(2^.5)/2---x+Pi/4=2kPi+'-Pi/4---x=2kPi;2kPi-Pi/2.(k是整數(shù))方程的解集是:{x|x=2kPi;2kPi-Pi/2;kPi-Pi/4.k是整數(shù)}