(sin²t +2sin t*cos t-cos²t)² = 1-sin 4t посчитайте ​

sin 2x = 2 sin x * cos x

cos 2x = cos² x - sin² x

cos² x + sin² x = 1

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(sin²t +2sin t*cos t-cos²t)² = (sin²t-cos²t +2sin t*cos t)² = (sin 2t - cos 2t)² =

= sin² 2t - 2 sin 2t cos 2t + cos² 2t = 1-sin 4t