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cos4x=cos2x |
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Answer» Cos4x = cos2x Using formula : cos2a = 2cos²a - 1 2cos²2x - 1 = cos2x ⇒ 2cos²2x - cos2x -1 = 0⇒ 2cos²2x - 2cos2x + cos2x - 1 = 0⇒ 2cos2x(cos2x-1 ) + 1 (cos2x-1) = 0⇒ (cos2x-1)(2cos2x + 1) = 0⇒ cos2x = 1⇒ 2x = 2nπ +- 0 ⇒ x = nπ or cos2x = -1/2⇒ 2x = 2nπ +- 2π/3 ⇒ x = nπ +- π/3 Intersection : x ∈ nπ U nπ +- π/3 |
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