Question

sin4 2x + cos4 2x = 5/8 В ответе указать ( в градусах) число корней на промежутке [0; 180] градусов/ Срочно помогите, пожалуйста

Answer 1

(1-сos4x)²/4+(1+cos4x)²/4=5/8
2-4cos4x+2cos²4x+2+4cos4x+2cos²4x=5
4cos²4x=1
4(1+cos8x)/2=1
2+2cos8x=1
2cos8x=-1
cos8x=-1/2
8x=-2π/3+2πk U 8x=2π/3+2πk
x=-π/12+πk/4 U x=π/12+πk/4,k∈z
0≤-π/12+πk/4≤π U 0≤π/12+πk/4≤π
0≤-1+3k≤12 U 0≤1+3k≤12
1≤3k≤13 U -1≤3k≤11
1/3≤k≤13/3
k=1⇒x=-π/12+π/4=π/6
k=2⇒x=-π/12+π/2=5π/12
k=3⇒x=-π/12+3π/4=2π/3
k=4⇒x=-π/12+π=11π/12
0≤-1+3k≤12 U 0≤1+3k≤12 
-1≤3k≤11
-1/3≤k≤11/3
k=0⇒x=π/12
k=1⇒π/12+π/4=π/3
k=2⇒x=π/12+π/2=7π/12
k=3⇒x=π/12+3π/4=5π/6