IrkaShevko

Verified answer

(sin²2x + cos²2x)(sin⁴2x - cos²2xsin²2x + cos⁴2x) = 7/16

(sin²2x + cos²2x)² - 3cos²2xsin²2x = 7/16

1 - 3cos²2xsin²2x = 7/16

3cos²2xsin²2x = 9/16

cos²2x(1-cos²2x) = 3/16

cos²2x - cos⁴2x = 3/16

16cos⁴2x - 16cos²2x + 3 = 0
D = 256 - 192 = 64 = 8²

cos²2x = (16 - 8)/32 = 1/4

cos2x = -1/2
2x = +- 5π/6 + 2πk, k∈Z
x = +- 5π/12 + πk, k∈Z

cos2x = 1/2
2x = +- π/6 + 2πk, k∈Z
x = +- π/12 + πk, k∈Z

cos²2x = (16 + 8)/32 = 3/4

cos2x = -√3/2
2x = +- 2π/3 + 2πk, k∈Z
x = +- π/3 + πk, k∈Z

cos2x = √3/2
2x = +- π/3 + 2πk, k∈Z
x = +- π/6 + πk, k∈Z

Ответ: +- 5π/12 + πk, k∈Z; +- π/12 + πk, k∈Z; +- π/3 + πk, k∈Z; +- π/6 + πk, k∈Z