知道f(sin x/2 )=2+cosx 求f(cos x/2 )

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/04 18:21:14
知道f(sin x/2 )=2+cosx 求f(cos x/2 )

知道f(sin x/2 )=2+cosx 求f(cos x/2 )
知道f(sin x/2 )=2+cosx 求f(cos x/2 )

知道f(sin x/2 )=2+cosx 求f(cos x/2 )
f(sin(x/2))=2+cosx=2+(1-2sin²(x/2)=3-2sin²(x/2)
f(cos(x/2)=3-2cos²(x/2)=3-(1+cosx)=2-cosx


f(sin x/2 )=2+cosx=2+1-2sin²(x/2)=3-2sin²(x/2)
∴ f(t)=3-2t²
∴ f(cosx/2)=3-2*cos²(x/2)=2-[2cos²(x/2)-1]=2-cosx


f(cosx/2)=f[sin(90°-x/2)]=2+cos(90°-x/2)=2+sinx/2