f（x）=cos^x/2—sin^x/2+sinx当xo∈（0,π/4）且f（x0）=4根2/5,求f（x0+π/6）的值

Question

f（x）=cos^x/2— sin^x/2+sinx 当xo∈（0,π/4）且f（x0）=4根2/5,求f（x0+π/6）的值

Answer 1

f(x)=(cos(x/2))^2 /2 -(sin(x/2))^2+sinx
=cosx+sinx
=√2sin(x+π/4 )
f(x0)= √2sin(x0+π/4 )=4√2/5
sin(x0+π/4)=4/5 cos(x0+π/4)=3/5
f(x0+π/6)=sin[(x0+π/6)+π/4]=sin[(x0+π/4)+π/6]=(4/5)(√3/2)+(3/5)*(1/2)=(4√3+3)/10