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6.Solvethe following t-equations(G)sin 2x + sin 6x + sin 4x0(i |
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Answer» recall that: sinA + sinB = 2sin[(A + B)/2] cos[(A - B)/2] 0 ≤ x < 2π then 0 ≤ 2x < 4π 0 ≤ 4x < 8π sin(2x) + sin(4x) + sin(6x) = 0 let y = 2x we have: siny + sin2y + sin3y = 0 sin3y + siny + sin2y = 0 2sin[(3y + y)/2] cos[(3y - y)/2] + sin2y = 0 2sin2y cosy + sin2y = 0 sin2y (2cosy + 1) = 0 sin2y = 0, cosy = -1/2 sin4x = 0, cos2x = -1/2 4x = 0, π, 2π, 3π, 4π, 5π, 6π, 7π OR 2x = 2π/3, 4π/3, 8π/3, 10π/3 x = 0, π/4, π/2, 3π/4, π, 5π/4, 3π/2, 7π/4 OR x = π/3, 2π/3, 4π/3, 5π/3 x = 0, π/4, π/2, 3π/4, π, 5π/4, 3π/2, 7π/4, π/3, 2π/3, 4π/3, 5π/3 x = 0, π/4, π/3, π/2, 2π/3, 3π/4, π, 5π/4, 4π/3, 3π/2, 7π/4, 5π/3 ⇦ ANSWER |
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