Y=4(cos⁡x )^2+4√3 sin⁡x cos⁡x-2
=2cos⁡2x+4√3 sin⁡x cos⁡x
=4sin⁡〖(2x+〗 π/6)
\x09由上可得,函數(shù)最大值為4,此時(shí)x的值為x= π/3+k π(k為一切整數(shù))
\x09函數(shù)在［-π/2,π/2］上單調(diào)遞增；在（(π/2,3 π)/2)上單調(diào)遞減,
因此此函數(shù)的單調(diào)遞增區(qū)間為［-π/3+kπ,π/3+kπ］,單調(diào)遞減區(qū)間為(π/3+kπ,2π/3+kπ)