F4 maths problem( Trigonometric )

Solve the following equations for 0°≦θ＜360°.
1. ( sinθ + cosθ )(sinθ - cosθ) = 1

(sinθ + cosθ)(sinθ - cosθ) = 1

sin2θ - cos2θ = 1 【Using identity a2-b2=(a-b)(a+b)】

cos2θ - sin2θ = -1

cos2θ = -1 【Using identity cos2A = cos2A-sin2A】

2θ = π or 2θ = 3π

θ = π/2 or θ = 3π/2

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2. 1/sinθ + sinθ - 2 = 0

1/sinθ + sinθ - 2 = 0 【Assume sinθ not equals to 0】

1 + sin2θ - 2sinθ = 0

sin2θ - 2sinθ + 1 = 0

(sinθ - 1)2 = 0

sinθ - 1 = 0

sinθ = 1

θ = π/2

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3. cos2θ = sinθ ( 1 + sinθ )

cos2θ = sinθ(1 + sinθ)

cos2θ = sinθ + sin2θ

1 - sin2θ = sinθ + sin2θ 【Using identity sin2A+cos2A=1】

2sin2θ + sinθ - 1 = 0

(2sinθ - 1)(sinθ + 1) = 0

2sinθ - 1 = 0 or sinθ + 1 = 0

sinθ = 1/2 or sinθ = -1

θ = π/6 or θ = 5π/6 or θ = 3π/2

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4.cos4θ - 3cos2θ + 2 = 0

cos4θ - 3cos2θ + 2 = 0

(cos2θ - 2)(cos2θ - 1) = 0

cos2θ - 2 = 0 or cos2θ - 1 = 0

cos2θ = 2 (rejected as 0 ≦ cos2θ ≦ 1) or cos2θ = 1

cosθ = 1 or cosθ = -1

θ = 0 or θ = π