Question

已知函数f(x)=sinx/2cosx/2+cos平方x/2-1/2

(1)求函数f（x）的最小正周期及对称轴方程
（2）若f（a）=-2根号2/5 a∈[5π/4,3π/2] 求cos(2a+π/4)的值

Answer 1

(1)f(x)=根号2/2sin(x+π/4)
T=2π，x+π/4=π/2+kπ,所以对称轴为x=π/4+kx,k∈Z
（2）f(a)=根号2/2sin(a+π/4)=-2根号2/5
所以sin(a+π/4)=-2/5,
a∈[5π/4,3π/2] ,所以a+π/4∈[3π/2,7π/4]
cos（a+π/4）=根号21/5
所以cos2a=sin（2a+π/2)=2sin(a+π/4)cos(a+π/4)=-4根号21/25
sin2a=-cos(2a+π/2)=2cos^2(a+π/4)-1=17/25
cos(2a+π/4)=根号2/2（cos2a-sin2a)=-4根号42/50-17根号2/50