Watch dance
get up
Go
eat
Listent
will
cook
Let
at home.
1. My sister hates listening to CDs - but she really enjoys
DVDs.
2. My parents don't like
out in restaurants. They prefer
3. I don't mind
early in the summer, when it's light in the mornings.
4. Jane wanted
to the party and he parents finally agreed
5. I love
and I
a dancer when o leave school.
her go.​

Во-первых, если cos x = 2√2/3, то cos^2 x = 8/9, sin^2 x = 1/9; sin x = 1/3.
cos^2 (x-38) + cos^2 38 - 2cos(x-38)*cos x*cos 38 =
= (cos x*cos 38+sin x*sin 38)*cos(x-38) + cos^2 38 - 2cos(x-38)*cos x*cos 38
= cos^2 38 + cos(x-38)*sin x*sin 38 + cos(x-38)*cos x*cos 38 -
- 2cos(x-38)*cos x*cos 38 =
= cos^2 38 + cos(x-38)*sin x*sin 38 - cos(x-38)*cos x*cos 38 =
= cos^2 38 - cos(x-38)*(cos x*cos 38 - sin x*sin 38) =
= cos^2 38 - cos(x-38)*cos(x+38) =
= cos^2 38 - 1/2*(cos(x-38-x-38) + cos(x-38+x+38)) =
= cos^2 38 - 1/2*(cos 76 + cos 2x) =
= cos^2 38 - cos 38*sin 38 - cos^2 x + 1/2 =
= cos 38*(cos 38 - sin 38) - 8/9 + 1/2 = cos 38*(cos 38 - sin 38) - 7/18
Дальше не знаю. Проверил калькулятором - получается какое-то иррациональное число, примерно равное -0,253.

Пошаговое объяснение:

В основном используется табличный интеграл от степенной функции, да ещё от синуса.

\int\limits {x^n} \, dx =  \frac{1}{n+1} x^{n+1} +C \\  \\  \int\limits {sinx} \, dx = -cosx + C

1а. f(x)=2-x

\int\limits {(2-x)} \, dx = 2* \frac{1}{0+1} x^{0+1} - \frac{1}{1+1}x^{1+1} + C = 2x - \frac{1}{2} x^2 +C

2б. f(x)=x^4 - sin x

\int\limits {(x^4 - sin x)} \, dx =  \frac{1}{4+1}x^{4+1} -(-cosx) +C =  \frac{1}{5}  x^5+ cosx +C

2в. f(x)= 2/ x^3

\int\limits { \frac{2}{x^3} } \, dx = \int\limits { 2x^{-3} \, dx = 2* \frac{1}{-3+1} x^{-3+1} + C = -x^{-2} + C = - \frac{1}{x^2} + C