For the first one, look at the graphs of sin(x) and cos(x). If you notice, they're the same thing but sin(x) is just cos(x), but phase-shifted +90 degrees. (It's 90 degrees 'ahead' of cos(theta).
If you think about cos(90 - x), what that's really saying is 'take cos(x), shift it 90 degrees to the left, and then flip it over the y-axis'. If you draw out cos(x) and do this, you'll quickly notice that the graph you get is the exact same thing as sin(x). Thus, cos(90-x) = sin(x) = 4/5, as given in the question.
Second one is just algebra.
R = F / (N + F)
We want an equation that says F = <the rest of the stuff>
so we do this:
R(N+F) = F
RN + RF = F
RN = F - RF
RN = F(1-R)
RN/(1-R) = F
So answer B.
The third question is a quadratic equation question. You have basically two options for how to deal with these: either google how to make a calculator program that will solve the roots for you, or memorize the equation.
For functions that look like ax^2 + bx + c = 0, there are generally only one or two values of 'x' that when you plug them into the left-hand side of the equation, it comes out equaling zero. To find them, you use the quadratic formula
https://www.youtube.com/watch?v=2lbABbfU6Zc(it's a patronizing song but it works)
By doing this, you get two roots: 4 - 2*sqrt(3) and 4 + 2*sqrt(3). Add them both together and you get 8.