Question

已知函数f(x)=.

(1)化简f(x)，并求f()；

(2)若0＜α＜π，f(α)+f()=0,求α.

Answer 1

解：(1)f(x)==|sin²|-|cos²-2|

=(2-sin²)-(2-cos²)=cos²-sin²=cosx,                                    

∴f()=cosπ=cos=.                                                

(2)由f(α)+f()=cosα+cos=0,即2cos²+cos-1=0,

∴cos=-1或cos=,∵0＜α＜π,                                             ∴=,α=π.