(cosα-sinα)²=(√0,8)²
cos²α-2cosαsinα+sin²α=0,8
1-sin2α=0,8
sin2α=1-0,8=0,2
cos²2α=1-sin²2α
cos²2α=1-0,04=0,96
cos4α=cos²2α-sin²2α=0,96-0,04=0,92
G+5x+9x^2= 9x^2+5x+g= (3x)^2 +2*3x*5/6+(5/6)^2= (3x+5/6)^2;
g=(5/6)^2=25/36
<span>Решение
</span>ctgx+cos(pi/2+2x)=0
<span>ctgx-sin2x=0
cosx/sinx - 2sinxcosx = 0 * (sinx </span>≠ 0, x ≠ πk, k ∈ Z)
cosx - 2sin²xcosx = 0
cosx(1 - 2sin²x) = 0
1) cosx = 0
x = π/2 + πn, n ∈ Z
2) 1 - 2sin<span>²x = 0
</span> 2sin<span>²x = 1
</span>sin²x = 1/2
sinx = - √2/2
x = (-1)^(n)(5π/4) + πn, n ∈ Z
sinx = √2/2
x = (-1)^(n)(π/4) + πn, n ∈ Z
Ответ: x = π/2 + πn, n ∈ Z; x = (-1)^(n)* (5π/4) + πn, n ∈ Z;
<span>x = (-1)^(n)* (π/4) + πn, n ∈ Z</span>
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