已知函数f(x)=sin2x+cox2x,x属于R.求f(x)的单调递增区间.
问题描述:
已知函数f(x)=sin2x+cox2x,x属于R.求f(x)的单调递增区间.
答
f(x)=sin2x+cos2x=(根号2)*sin(2x+π/4), 要使其递增, 则(2x+π/4)∈[-π/2+2kπ,π/2+2kπ]
则x∈[-3π/8+kπ,π/8+kπ]
答
f(x)=sin2x+cos2x
=√2(√2/2*sin2x+√2/2cos2x)
=√2(sin2xcosπ/4+cos2xsinπ/4)
=√2sin(2x+π/4)
"递增则2kπ-π/2