(1) f(x)=cos3x/2 cosx/2 -sin3x/2 sinx/2-2sinxcosx
=cos(3x/2 +x/2)-sin2x
=cos2x-sin2x
=-√2sin(2x-π/4).
f(x)的最少正周期是 2π/2,即π.
(2) 当x∈[π/2,π]时,2x-π/4∈[3π/4,7π/4],
在[3π/4,7π/4]内,使f(x)=0的值是π,
由2x-π/4=π,得x=5π/8.
即函数f(x)的零点是x=5π/8.
(1) f(x)=cos3x/2 cosx/2 -sin3x/2 sinx/2-2sinxcosx
=cos(3x/2 +x/2)-sin2x
=cos2x-sin2x
=-√2sin(2x-π/4).
f(x)的最少正周期是 2π/2,即π.
(2) 当x∈[π/2,π]时,2x-π/4∈[3π/4,7π/4],
在[3π/4,7π/4]内,使f(x)=0的值是π,
由2x-π/4=π,得x=5π/8.
即函数f(x)的零点是x=5π/8.