已知函数f(x)=sinx/2cosx/2+cos^2(x/2)-1/2

已知函数f(x)=sinx/2cosx/2+cos^2(x/2)-1/2.
(1)若f(a)=√2/4,a∈(0,π),求a的值
(2)求函数f(x)在[-π/4,π]上的最大值和最小值
f(x)=sin(x/2)cos(x/2)+cos^2(x/2)-(1/2)
=(1/2)×sinx+(1/2)×(cosx+1)-(1/2)
=(1/2)×(sinx+cosx)
=(√2/2)×sin(x+(π/4))
(1)若f(a)=√2/4=(√2/2)×sin(a+(π/4))
则sin(a+(π/4))=1/2,a+(π/4)=2kπ+(π/2)±((2π)/3)；
又a∈(0,π),则a=π/12或(5π)/12；
(2)当x∈[-π/4,π]上时,x+(π/4)∈[0,(5π)/4],
则当x+(π/4)=π/2,即x=π/4时,f(x)max=√2/2；
则当x+(π/4)=(5π)/4,即x=π时,f(x)max=-1/2.