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In complex number ( especially for any real number) x and integer n it holds that (cos(x) + i(sinx))^n = cos(n x) + isin(n x) where i is the imaginary unit representing as i*i = -1. This is called De Moivre'...

Here, we must remember the definition of a bijection. To be bijective, a function must be both injective and surjective. For a function to be injective, we must have that f(a) = f(b) implies that a = b. For ...

This question relies partially on remembering the trigonometric identities, csc(x) = 1/(sin(x)) and cot(x) = 1/(tan(x)) = cos(x)/sin(x). Plugging these values into the equation, we want to find Lim((1-cos(x)...

For this question, we want to start by finding the possible values of a from the first equation and then using that to give us information about b from the second equation. Now, the condition that a^2 < 4...

At first glance, this may look like an inverse trig integral but as the top contains an x term, we must use a different method. First, rewrite the top in two parts, one that is a multiple of the derivative o...