Question

упростите выражение : cos ²2 x+(1+cos2x)²tg²x​

Answer 1

Ответ:

${cos}^{2}2x + (1 + cos2x)^{2} {tg}^{2} x = \\ = cos^{2} 2x + ( {sin}^{2} x + {cos}^{2} x + {cos}^{2} x - {sin}^{2} x)^{2} {tg}^{2} x = \\ = {cos}^{2} 2x +4{cos}^{4}x \frac{ {sin}^{2} x}{ {cos}^{2} x } = \\ = {cos}^{2}2x + 4 {cos}^{2} x {sin}^{2} x = \\ = {cos}^{2} 2x + {sin}^{2}2x = 1$