cosx=±√(1-sinx^2)=±√(1-1/4)=±√3/2
tanx=sinx/cosx=±√3/3
y=1-1/2cos(2x+派/4)取得最大值
就要使cos(2x+π/4)取得最小值-1
即 2x+π/4=2kπ+π
x+π/8=kπ+π/2
x=kπ+3π/8,k∈z
y最大值为1+1/2=3/2
自变量x的集合为{x|x=x=kπ+3π/8,k∈z}
y=1-1/2cos(2x+派/4)取得最小值
就要使cos(2x+π/4)取得最大值1
即 2x+π/4=2kπ
x+π/8=kπ
x=kπ-π/8,k∈z
y最小值为1-1/2=1/2
自变量x的集合为{x|x=kπ-π/8,k∈z}
sin25/6派+cos25/3派+tan(-25/4派)+sin(26/3派)
=sin(4π+π/6)+cos(8π+π/3)-tan(6π+π/4)+sin(8π+2π/3)
=sinπ/6+cosπ/3-tanπ/4+sin2π/3
=1/2+1/2-1+√3/2
=√3/2