已知f(x)=√2sin(2x+π/4)+√2求F(x)=f(x)-f(x-π/4)的最大值,若F(a)=6/5,求sina._数学解答

已知f(x)=√2sin(2x+π/4)+√2
求F(x)=f(x)-f(x-π/4)的最大值,若F(a)=6/5,求sina.

人气：177 ℃　时间：2020-06-02 11:36:48

解答

F(x)=f(x)-f(x-π/4)
=√2sin(2x+π/4)+√2-√2sin(2(x-π/4)+π/4)-√2
=√2sin(2x+π/4)-√2sin(2x-π/4)
=√2sin2x*√2/2+√2cos2x*√2/2-(√2sin2x*√2/2-√2cos2x*√2/2)
=sin2x+cos2x-sin2x+cos2x
=2cos2x
-1