Question

sin^4(x)+cos^4(x)=cos^2(2x)+1/4

Answer 1

Ответ: (1-сos2x)²/4+(1+cos2x)²/4-cos²2x-1/4=0

1-2cos2x+cos²2x+1+2cos2x+cos²2x-4cos²2x-1=0

1-2cos²2x=0

cos²2x=1/2

cos2x=-1/2⇒2x=+-2π/3+2πk⇒x=+-π/3+πk,k∈z

cos2x=1/2⇒2x=+-π/3+2πk⇒x=+-π/6+πk,k∈z

Объяснение: