已知f(x)=√2sin(x+π/4),当x0∈(0,π/4),且f(0)=(4√2)/5时,求f(x0+π/6)的值已知f(x)=√2sin(x+π/4),当x0∈(0,π/4),且f(0)=(4√2)/5时,求f(x0+π/6)的值.

问题描述:

已知f(x)=√2sin(x+π/4),当x0∈(0,π/4),且f(0)=(4√2)/5时,求f(x0+π/6)的值
已知f(x)=√2sin(x+π/4),当x0∈(0,π/4),且f(0)=(4√2)/5时,求f(x0+π/6)的值.

f(x)=√2sin(x+π/4)=sinx+cosxf(xo+π/6)=sin(xo+π/6)+cos(xo+π/6)=0.5cosxo+√3/2sinxo+√3/2cosxo-0.5sinxosinxo+cosxo=(4√2)/5 (sinxo+cosxo)^2=32/25 2sinxocosxo=7/25(cosxo-sinxo)^2=18/25 cosxo-sinxo=...