問30
(1)
sin θ = 2sin θ cos θ
sin θ(1-2cos θ)=0
sin θ=0, cos θ=1/2
θ=0, π/3, π, 5π/3
(2)
sin θ - (cos^{2}θ-sin^{2}θ)=0
sin θ - (1-sin^{2}θ-sin^{2}θ)=0
2sin^{2}θ+sin θ -1=0
(2sin θ -1)(sin θ + 1)=0
sin θ = 1/2, sin θ = -1
θ = π/6, 5π/6, 3π/2
(3)
cos^{2}θ - sin^{2}θ - 3cos θ - 1 = 0
2cos^{2}θ-3cos θ - 2=0
(2cos θ+1)(cos θ -2) = 0
cos θ = -1/2
θ = 2π/3, 4π/3
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