f(X)=SIN平方θ+sin平方(θ+β),其中α β

显示全部楼层 · 2011-2-7 12:42:10

写点很丑

千问 · 2011-2-7 12:42:10

f(x)=sin^2θ+sin^2(θ+α)+sin^2(θ+β)=1/2(1-cos2θ）+1/2[1-cos(2θ+2α)]+1/2[1-cos(2θ+2β)]=3/2-1/2cos2θ-1/2[cos(2θ+2α)+cos(2θ+2β)]=3/2-1/2cos2θ-cos[(2θ+2α+2θ+2β)/2] * cos[(2θ+2α-2θ-2β)/2]=3/2-1/2cos2θ-cos(2θ+α+β) * cos(α-β)=3/2-1/2cos2θ-cos(2θ+α+β) * cos(β-α)当1/2cos2θ+cos(2θ+α+β) * cos(β-α)=0时f(θ)=3/2为定值，此时：∵0≤α＜β＜π∴0＜α+