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secondary 3 | A Maths
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Date Posted: 2 years ago
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(a)
sin2x -= 2sinx•cosx
2sinx•cosx - sinx = 0
sinx•(2cosx - 1) = 0
⇨
sinx = 0
⇨ x₁ = 0° ; x₂ = 180° ; x₃ = 360°
cosx = ½
⇨ x₄ = 60° ; x₅ = 300°
sin2x -= 2sinx•cosx
2sinx•cosx - sinx = 0
sinx•(2cosx - 1) = 0
⇨
sinx = 0
⇨ x₁ = 0° ; x₂ = 180° ; x₃ = 360°
cosx = ½
⇨ x₄ = 60° ; x₅ = 300°
(b)
cos2x = 1 - 2sin²x
sinx = a
1 - 2a² = 1 - 3a
2a² - 3a = 0
a(2a-3) = 0
a = sinx = ³⁄₂ (✗✗✗) 【sinθ ≤1】
a = sinx = 0
⇨ x₁ = 0° ; x₂ = 180° ; x₃ = 360°
cos2x = 1 - 2sin²x
sinx = a
1 - 2a² = 1 - 3a
2a² - 3a = 0
a(2a-3) = 0
a = sinx = ³⁄₂ (✗✗✗) 【sinθ ≤1】
a = sinx = 0
⇨ x₁ = 0° ; x₂ = 180° ; x₃ = 360°
(c)
tan(x/2) = (1-cosx)/sinx
(1-cosx) = sin²x = 1 - cos²x
cosx • (cosx-1) = 0
cosx = 0 ⇨ x₁ = 90° ; x₂ = 270°
cosx = 1 ⇨ x₃ = 0° ; x₄ = 360°
tan(x/2) = (1-cosx)/sinx
(1-cosx) = sin²x = 1 - cos²x
cosx • (cosx-1) = 0
cosx = 0 ⇨ x₁ = 90° ; x₂ = 270°
cosx = 1 ⇨ x₃ = 0° ; x₄ = 360°
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