Question

If cos² θ + cos θ = 0 find the value of θ.

Answer 1

cos² θ + cosθ = 0

cosθ( cosθ + 1 ) = 0

cosθ = 0

Therefore, θ = 90°

cosθ + 1 = 0

cosθ = -1

Therefore, θ = 180°

Answer 2

• cos² θ + cos θ = 0
• cosθ (cosθ + 1) = 0
• Case 1 : cosθ = 0
• => cosθ = cos90°
• => θ = 90°
• Case 2 : cosθ + 1 = 0
• cosθ = -1
• cosθ = cos180°
• => θ = 180°
• ∴ θ = 90° , 180°

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