已知sin(A+π/4)=7√2/10,A∈(0,π/4)

问题描述:

已知sin(A+π/4)=7√2/10,A∈(0,π/4)
⑴求cosA的值 ⑵求函数f(x)=cos2x+5cosAcosx+1的值域

[1] sin(A+π/4)=sinAcos(π/4)+cos(π/4)sinA=7√2/10即sinA=7/5-cosA平方化简(cosA)^2-(7/5)cosA+12/25=0A∈(0,π/4)cosA=4/5[2] f(x)=2(cosx)^2+4cosx=2[cosx+1]^2-2∵-1≤cosx≤1∴f(x)∈[-2,6]