Решение смотри в приложении
1) sin^2 a - 5sin a*cos a + 4cos^2 a = 0
Делим все на cos a
tg^2 a - 5tg a + 4 = 0
(tg a - 1)(tg a - 4) = 0
tg a = 1; a1 = pi/4 + pi*k
tg a = 4; a2 = arctg(4) + pi*n
2)
![\int\limits^2_1 { \frac{2x^2+1}{x} } \, dx = \int\limits^2_1 (2x+ \frac{1}{x} ) \, dx =(x^2+ln|x|)|^2_1=(4+ln2)-(1+ln1)=](https://tex.z-dn.net/?f=+%5Cint%5Climits%5E2_1+%7B+%5Cfrac%7B2x%5E2%2B1%7D%7Bx%7D+%7D+%5C%2C+dx+%3D+%5Cint%5Climits%5E2_1+%282x%2B+%5Cfrac%7B1%7D%7Bx%7D+%29+%5C%2C+dx+%3D%28x%5E2%2Bln%7Cx%7C%29%7C%5E2_1%3D%284%2Bln2%29-%281%2Bln1%29%3D)
![=3+ln2-ln1=3+ln2](https://tex.z-dn.net/?f=%3D3%2Bln2-ln1%3D3%2Bln2)
А) а2=а1+d=7
a3=a1+2d=a2+d=14
a4=a3+d=21
a5=a1+4d=a4+d=28
a6=a1+5d=a5+d=35
a7=a1+6d=a6+d=42
б)a2=a1+d=1
a3=a1+2d=a2+d=5
a4=9
a5=13
a6=17
a7=21