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Truthfully, the notation $\cos^2(x)$ should actually mean $\cos(\cos(x)) = (\cos \circ \cos)(x)$, that is, the 2nd iteration or compositional power of $\cos$ with itself, because on an arbitrary space of self-functions on a given set, the natural "multiplication" operation is composition of those functions, and the power is applied to the function symbol itself, not the whole evaluation ...
$\sin^{4}x+\cos^{4}x$ I should rewrite this expression into a new form to plot the function. \begin{align} &; = (\sin^2x)(\sin^2x) - (\cos^2x)(\cos^2x) \\ & ...
21 kwi 2015 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
$\begingroup$ When you have a doubt like this and you are lazy to find a formal proof that concludes that your hyphotesis is true, you can probe a few random values until you find a counterexample that invalidate the hyphotesis of your question.
the same diagram also gives an easy demonstration of the fact that $$ \sin 2x = 2 \sin x \cos x $$ as @Sawarnak hinted, with the help of this result, you may apply your original idea to use calculus for an easy derivation, since differentiation gives $$ 2 \cos 2x = 2(\cos^2 x - \sin^2 x) $$ it is not a bad idea to familiarize yourself with several different 'proofs' of such fundamental ...
Question: Solve $\sin(3x)=\cos(2x)$ for $0≤x≤2\pi$. My knowledge on the subject; I know the general identities, compound angle formulas and double angle formulas so I can only apply those.
29 lip 2017 · The answers from the back of the book says the answers are $\\pi/2$ and $3\\pi/2$. I thought that you can use the double angle formula in this problem, but it doesn't seem right?
Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
30 lip 2017 · I'll need to memorize $\cos2x = \cos^2x - \sin^2x$ as I'll use it in derivatives. Only, there are other forms for this identity, I can't see how I can get to the others from this one above. The other forms are. $$2\cos^2x - 1\\ 1 - 2\sin^2x$$
15 cze 2016 · How to I find the antiderivative of $\cos^2x$? I have tried partial integration, it doesn't seem to work (for me). Some help on how to integrate it would be nice.
