有a.maths 唔識做

1) sin2 θ + 1/2sin2 2θ = 1
sin2 θ + 2sin2 θcos2θ = 1
sin2 θ + 2sin2 θcos2θ -1=0
sin2 θ + 2sin2 θcos2θ -(sin2θ+cos2θ)=0
2sin2 θcos2θ-cos2θ=0
cos2θ( 2sin2 θ-1)=0
cos2θ=0 or sin2 θ=1/2
cosθ=0 or sinθ= 1/√2
θ=45˚,90˚,135˚,225˚,270˚,315˚

2) 3 - 4cos2θ + cos4θ = 1/2
3 - 4cos2θ + (2cos22θ-1) = 1/2
2- 4cos2θ + 2cos22θ = 1/2
2cos22θ- 4cos2θ -3/2=0
4cos22θ- 8cos2θ+3=0
(2cos2θ-3)(2cos2θ-1)=0
cos2θ=3/2(reject) or cos2θ=1/2
2θ=60˚,300˚,420˚ or 660˚
θ=30˚,150˚,210˚ or 330˚