Sin^6 (x) + cos^6 (x) = (5/4) sin^2 (2x)

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Алгебра

Васяша

18 декабря, 13:49

Sin^6 (x) + cos^6 (x) = (5/4) sin^2 (2x)

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Ануфрий · Answer 1

sin^6 (x) + cos^6 (x) = (5/4) sin^2 (2x)

sin^6 (x) + cos^6 (x) = 5 sin^2 (x) * cos^2 (x)

(sin^2 (x) + cos^2 (x)) (sin^4 (x) + cos^4 (x) - sin^2 (x) cos^2 (x)) = 5/4sin^2 (2x)

1/8 (3cos (4x) + 5) = - 5/8 (cos (4x) - 1)

cos (4x) = 0

x = πn - (7π) / 8

x = πn - (5π) / 8

x = πn - (3π) / 8

x = πn-π/8

n ∈ Z