x属于(π/4,π/2),且(4cosx-3sinx)(2cosx-3sinx)=0求tan(x + π/4)
问题描述:
x属于(π/4,π/2),且(4cosx-3sinx)(2cosx-3sinx)=0求tan(x + π/4)
答
(4cosx-3sinx)(2cosx-3sinx)=0所以cosx=(3/4)sinx,cosx=(3/2)sinxx属于(π/4,π/2),所以sinx>cosx>0所以cosx=(3/2)sinx不成立所以cosx=(3/4)sinxtanx=sinx/cosx=4/3tan(x+π/4)=(tanx+tanπ/4)/(1-tanxtanπ/4)=-7...