Question

1. 3/cos^2 24+cos^2 114.
2. Sin5x=3
3. 2cos(x/3-π/2)=2

Answer 1

2*cos²(4x)-6*cos²(2x)+1=0
2(2cos²2x-1)²-6*cos²(2x)+1=0
cos²2x = y
2(2y-1)²-6y+1=0
2(4y²-4y+1)-6y+1=0
8y²-8y+2-6y+1=0
8y²-14y+3=0
D=14²-4*8*3 = 196-96 = 100
y1=(14+√100)/(2*8) = 24/16 = 3/2
y2=(14-√100)/(2*8) = 4/16 = 1/4
y = cos²2x =>
0≤y≤1 =>
y = 1/4
cos²2x = 1/4
cos2x1 = 1/2; cos2x2 = -1/2
2x1 = π/3
2x2 = 2π/3
x1 = π/6
x2 = π/3