Cos²(π/4+2a)=(1+cos(π/2+4a))/2=1/2-1/2*sin4a
sin²(π/4-2a)=(1-cos(π/2-4a))/2=1/2-1/2*sin4a
1/2-1/2*sin4a=1/2-1/2*sin4a
---------------------------------------
cos(π/2+a=-sina
cos(π/2-a)=sina
Решение
<span>{2x-3y=0 ,
{5x^2+2y=3
{3y = 2x
</span><span>{5x^2+2y=3
</span>
{y = (2/3) x
{5x² + 2*(2/3) x - 3 = 0 умножим на 3
{y = 2/3 x
<span>{15x² + 4x - 9 = 0
</span>
<span>15x² + 4x - 9 = 0
</span>D = 16 + 4*15*9 = 556
x₁ = (- 4 - 2√139)/30
x₁ = (- 2 - √139)/15
x₂ = <span> (- 4 + 2√139)/30</span>
x₂ = <span> (- 2 + √139)/15
</span>
<span>x₁ = (- 2 - √139)/15
</span>y₁ = (2/3) * (- 2 - √139)/15
y₁ = (- 4 - 2√139)/45
x₂ = (- 2 + √139)/15
y₂ = (2/3) * (- 2 + √139)/15
y₂ = <span>(- 4 + 2√139)/45
</span>
Ответ: x₁ = (- 2 - √139)/15 ; y₁ = (- 4 - 2√139)/45 ;
x₂ = (- 2 + √139)/15 ; y₂ = <span>(- 4 + 2√139)/45.</span>