Применяемое тригонометрическое тождество
<span>Cos4x = 1 - 2Sin²2x
</span><span>
1 - (1 - 2Sin²2x) = Sin2x</span>
2Sin²2x - Sin2x = 0
Sin2x(2Sin2x - 1) = 0
<span>Sin2x = 0 или 2Sin2x - 1 = 0
</span>1) Sin2x = 0
2x = πk, k∈Z<span>
x = πk/2
</span>2) 2Sin2x = 1
Sin2x = 1/2<span>
</span>
2x=(-1)^k πk/6+πk
x=(-1)^k πk/12+πk/2
X²-49+40<0
x²-9<0
(x-3)(x+3)<0
x=3 x=-3
x∈(-3;3)
D= - 4,9
a1 = - 0,2
a7 = a1 +6*d = - 0,2 - 6*4,9 =-0,2 - 29,4 = - 29,6