sin(A+π/4)=(7√2)/10,A属于(0,π/4) (1)求cosA (2)求函数f(x)=cos2x+5cosA*cosx+1的值域.

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sin(A+π/4)=(7√2)/10,A属于(0,π/4)(1)求cosA(2)求函数f(x)=cos2x+5cosA*cosx+1的值域.sin(A+π/4)=(7√2)/10,A属于(0,π/4

sin(A+π/4)=(7√2)/10,A属于(0,π/4) (1)求cosA (2)求函数f(x)=cos2x+5cosA*cosx+1的值域.
sin(A+π/4)=(7√2)/10,A属于(0,π/4) (1)求cosA (2)求函数f(x)=cos2x+5cosA*cosx+1的值域.

sin(A+π/4)=(7√2)/10,A属于(0,π/4) (1)求cosA (2)求函数f(x)=cos2x+5cosA*cosx+1的值域.
(1)sin(A+π/4)=√2/2sinA+√2/2cosA=(7√2)/10
sinA+cosA=7/5
sinA=7/5-cosA^2
sinA^2+cosA^2=1
(7/5-cosA)^2+cosA^2=1
因为A∈(0,π/4),所以 cosA=4/5
(2)f(x)=cos2x+5cosA×cosx+1
=cos2x+4cosx+1
=2cosx^2-1+4cosx+1
=2cosx^2+4cosx
设t=cosx
f(x)=2t^2+4t
因为t∈[-1,1] 所以f(x)∈[-2,6]

cosA =4/5;
值域为[-2,6]