作业帮【高一数学】已知函数f(x)=(cos^2)x/2-(sin^2)x/2+sinx
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【高一数学】已知函数f(x)=(cos^2)x/2-(sin^2)x/2+sinx
当x0∈(0,π/4)且f(x0)=4√2/5时,求f(x0+π/6)的值
当x0∈(0,π/4)且f(x0)=4√2/5时,求f(x0+π/6)的值
f(x)=(cos^2)x/2-(sin^2)x/2+sinx=(cos2*x/2)+sinx=sinx+cosx=√2sin(x+π/4)
f(x0)=√2sin(x0+π/4)=4√2/5
sin(x+π/4)=4/5
x0∈(0,π/4)则（x0+π/4）∈(π/4,π/2)
所以cos(x0+π/4)>0
cos(x0+π/4)=3/5
得f(x0+π/6)=√2sin(x0+π/4+π/6)
=√2[sin(x0+π/4)cosπ/6+cos(x0+π/4)sinπ/6]
=7√6/10
f(x0)=√2sin(x0+π/4)=4√2/5
sin(x+π/4)=4/5
x0∈(0,π/4)则（x0+π/4）∈(π/4,π/2)
所以cos(x0+π/4)>0
cos(x0+π/4)=3/5
得f(x0+π/6)=√2sin(x0+π/4+π/6)
=√2[sin(x0+π/4)cosπ/6+cos(x0+π/4)sinπ/6]
=7√6/10
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