Question

Bài 3: Tìm giá trị lớn nhất của hàm số: 2cos^2(x+π/4)-cos2x

Answer 1

`@TXĐ: RR`

`@y=2cos^2 (x+\pi/4)-cos 2x`

`y=2cos^2 (x+\pi/4)-1+1-cos 2x`

`y=cos(2x+\pi/2)+1-cos 2x`

`y=-sin 2x-cos 2x+1`

`y=-\sqrt{2}(1/\sqrt{2}sin 2x+1/\sqrt{2}cos 2x)+1`

`y=-\sqrt{2}sin(2x+\pi/4)+1`

Có: `-1 <= sin (2x+\pi/4) <= 1 AA x in RR`

`<=>\sqrt{2} >= -\sqrt{2}sin(2x+\pi/4) >= -\sqrt{2}`

`<=>\sqrt{2}+1 >= y >= -\sqrt{2}+1`

  `=>y_[max]=\sqrt{2}+1<=>sin(2x+\pi/4)=-1<=>2x+\pi/4=-\pi/2+k2\pi`

                                                    `<=>x=[-3\pi]/8+k\pi`  `(k in ZZ)`