Răspuns:
cos⁴x=(1-sin²x)²=1-2sin²x+sin⁴x
ecuatia devine
sin⁴x+1-2sin²x+sin⁴x=3/4
2sin⁴-2sin²x+1-3/4=0
2sin⁴-2sin²x+1/4=0
8sin⁴x-8sin²x+1=0
sin²x=y y≥0
Ecuatia devine
8y²-8y+1=0
Δ=8²-4*8=64-32=32
y1=(8-√32)/16=1/2-4√2/16=1/2-√2/4
y2=1/2+√2/4
sinx1=1/2-√2/4
x1=arcsin(1/2-√2/4)
x1=(-1)ⁿarcsin(1/2-√2/4)+nπ n∈Z
x2=(-1)ⁿarcsin(1/2+√2/4)+nπ
Explicație pas cu pas:
