【高一数学】已知函数f(x)=(cos^2)x/2-(sin^2)x/2+sinx

题目

【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

答案

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√2/5sin(x+π/4)=4/5x0∈(0,π/4)则（x0+π/4）∈(π/4,π/2)所以cos(x0+π/4)>0cos(x0+π/4)=3/5得f(x0+π/6)=...