Cos3x / (sin3x-2sinx) = tgx

Question

Математика

Германа

26 мая, 21:28

Cos3x / (sin3x-2sinx) = tgx

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Милий · Answer 1

Cos (3x) / (sin (3x) - 2sin (x)) = tg (x)

(4cos³ (x) - 3cos (x)) / (3sin (x) - 4sin³ (x) - 2sin (x)) = tg (x)

(cos (x) * (4cos² (x) - 3) / (sin (x) * (1 - 4sin² (x))) = tg (x)

cos (x) * (2cos (2x) - 1) / (sin (x) * (2cos (2x) - 1) = tg (x)

ctg (x) = tg (x) - - > tg (x) = ±1 - - > x = π/4 + πk/2, k - целое.