Основное тригонометрическое тождество
cos^2t+sin^2t=1
из этого следует, что cos^2t=1-sin^2,
а значит
<span>(1-sin^2t)(1+tg^2t)=1 </span>
cos^2t(1+tg^2t)=1
cos^2t+cos^2tg^2t=1
cos^2t+(cos^2t*sin^2t)/cos^2t=1
cos^2t+sin^2t=1
1=1
![-1 \leq cos(\alpha) \leq 1](https://tex.z-dn.net/?f=-1+%5Cleq+cos%28%5Calpha%29+%5Cleq+1)
- возможные значения косинуса
![2cos^2(x) - 5cos(x) + 3 = 0\\\\ 2cos^2(x) - 2cos(x)-3cos(x) + 3 = 0\\\\ 2cos(x)*(cos(x) - 1)-3*(cos(x) -1) = 0\\\\ (2cos(x) - 3)*(cos(x) -1) = 0\\\\ 2cos(x)-3=0\ \ or\ \ cos(x)-1=0\\\\ cos(x)=\frac{3}{2}\ \ or\ \ cos(x)=1\\\\ cos(x)=1\\\\ x=2\pi n,\ n\in Z](https://tex.z-dn.net/?f=2cos%5E2%28x%29+-+5cos%28x%29+%2B+3+%3D+0%5C%5C%5C%5C%0A2cos%5E2%28x%29+-+2cos%28x%29-3cos%28x%29+%2B+3+%3D+0%5C%5C%5C%5C%0A2cos%28x%29%2A%28cos%28x%29+-+1%29-3%2A%28cos%28x%29+-1%29+%3D+0%5C%5C%5C%5C%0A%282cos%28x%29+-+3%29%2A%28cos%28x%29+-1%29+%3D+0%5C%5C%5C%5C%0A2cos%28x%29-3%3D0%5C+%5C+or%5C+%5C+cos%28x%29-1%3D0%5C%5C%5C%5C%0Acos%28x%29%3D%5Cfrac%7B3%7D%7B2%7D%5C+%5C+or%5C+%5C+cos%28x%29%3D1%5C%5C%5C%5C%0Acos%28x%29%3D1%5C%5C%5C%5C%0Ax%3D2%5Cpi+n%2C%5C+n%5Cin+Z)
Ответ:
![2\pi n,\ n\in Z](https://tex.z-dn.net/?f=2%5Cpi+n%2C%5C+n%5Cin+Z)
X^8+y^8
надо было подобные подобрать вот и все
Решение:
1) ⁵√²⁸√а = (а^(1/28))^(1/5) = a^(1/28 * 1/5) = a^(1/140)
2) ⁷√²⁰√a = (a^(1/20))^(1/7) = a^(1/20 * 1/7) =a^(1/140)
3) ³⁵√⁴√a =(a^(1/4))^(1/35) = a^(1/4 * 1/35) = a^(1/140)
4) <u>15 a^(1/140) - 7a^(1/140) </u>=<u> 8a^(1/140) </u>= 4
2a^(1/140) 2^(1/140)
Ответ
4a^2-4a+1
x^2+6xy+9y^2
49-x^2
x^2+10x+25-10x+5x^2=6x^2+25
16-2y^2+16y-32= -2y^2+16y-16
a^4+8a^3+16a^2-a^4+4a^2-8a^3+4a^2=24a^2