Sin^4x/4-cos^4x/4=1/2

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Алгебра

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11 декабря, 20:38

Sin^4x/4-cos^4x/4=1/2

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Мана · Answer 1

(sin²x/4 + cos²x/4) · (sin²x/4 - cos²x/4) = 1/2

1 · (sin²x/4 - cos²x/4) = 1/2

- (cos²x/4 - sin²x/4) = 1/2

cos²x/4 - sin²x/4 = - 1/2

cos (2·x/4) = - 1/2

cos x/2 = - 1/2

x/2 = arccos (-1/2) + 2πn или x/2 = - arccos (-1/2) + 2πk

x/2 = (π - π/3) + 2πn x/2 = - (π - π/3) + 2πk

x = 4π/3 + 2πn x = - 4 π/3 + 2πk