f(x)=sin(2x+π/3)当tan(x+π/4)=1/3时,求f(x)

f(x)=sin(2x+π/3)当tan(x+π/4)=1/3时,求f(x)
f(x)=sin(2x+π/3)
当tan(x+π/4)=1/3时,求f(x)

f(x)=sin(2x+π/3)当tan(x+π/4)=1/3时,求f(x)
tan(x+π/4)=(1+tanx)/(1-tanx)=1/3 3+3tanx=1-tanx tanx=1/2 cos^2 x=1/sec^2 x=1/(1+tan^2 x)=1/(1+1/4)=4/5 sin^2x=1-cos^2x=1/5 cos2x=cos^2 x-sin^2 x=4/5-1/5=3/5 tan2x=2tanx/(1-tan^2x)=1/(1-1/4)=4/3 sin2x=cos2x*tan2x=4/5 f(x)=sin(2x+π/3) =sin2xcosπ/3+sinπ/3cos2x =4/5*1/2+√3/2*3/5 =(4+3√3)/10