已知函数f(x)=根号(sin(x/2)^4+4cos(x/2)^2)-根号(cos(x/2)^4+4sin(x/2)^2)(1)_数学解答

已知函数f(x)=根号(sin(x/2)^4+4cos(x/2)^2)-根号(cos(x/2)^4+4sin(x/2)^2)
(1)化简f(x),并求f(25π/6)
(2)若0<α<π,f(α)+f(α/2)=0,求α
（要过程啊~）

人气：144 ℃　时间：2019-10-11 20:29:35

解答

解1：f(x)=√[sin(x/2)^4+4cos(x/2)^2]-√[cos(x/2)^4+4sin(x/2)^2]=√{[1-cos(x/2)^2]^2+4cos(x/2)^2}-√{[1-sin(x/2)^2]^2+4sin(x/2)^2}=√[1+2cos(x/2)^2+cos(x/2)^4]-√[1-2sin(x/2)^2+sin(x/2)^4+4sin(x/2)^2]=...