For online material, I cannot recommend anything else but:
khanacademy.org
It has complete tutorials in the form of videos on almost anything, and exercises and solutions. You can also keep track of your progress and quiz yourself. It's an amazing resource.
Otherwise, in terms of books, the...
Suppose you have:
x \cdot a + x \cdot b = c
Then you clearly can't group the a and b together. However, this is what you can do:
x\cdot(a+b) = c
In your case:
\frac{3}{5} \cdot (cos^{2}(x) + sin^{2}(x)) =
\frac{3}{5} \cdot 1
I did not say that "symmetric functions" reach their maxima/minima when all of their values are equal, I said that if the constraints are symmetric, and the function is symmetric with respect to each parameter, then there is no reason that the solution would not be symmetric as well. It's a...
Yep, that's right! If it's a minimum, then picking any other values (Ex: a=0.7, b=0.2, c=0.1) will yield something higher than 9, always. So you're done now. But notice that you could have finished this problem in your head: if a+b+c=1, and the conditions on a,b,c are symmetric (all the same)...
There's no need for anything too fancy, here's how I would tackle it:
Notice that the conditions on a,b,c are symmetric, that is, consider this a problem of "optimization". Suppose I give you: Maximize x*y*z subject to x+y+z<=100, then you have a few options:
1 - Solve this problem using...