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 ...

In blue, a graph of the function $\color{blue}{\cos^2(x)}$ and in red a graph of the function $\color{red}{\cos(x^2)}$. Some say, a good plot is worth a million words! Share

Mar 14, 2016 · $\begingroup$ $\cos^2(x)$ may be misinterpreted as $\cos(\cos x)$, which is how you're supposed to interpret the exponent in $\cos^{-1}(x)$. It's confusing, but somehow the two meanings don't conflict that often, so it's a convension that is kept. $\endgroup$

Apr 25, 2017 · $$\cos (A + B)\cos (A - B) = {\cos ^2}A - {\sin ^2}B$$ I have attempted this question by expanding the left side using the cosine sum and difference formulas and then multiplying, and then simplif...

Apr 25, 2017 · Recall the formula $$\cos(2 \theta) = 2 \cos^2(\theta) - 1$$ This gives us $$\cos^2(\theta) = \dfrac{1+\cos(2 \theta)}{2}$$ Plug in $\theta = 2x$, to get what you want.

Oct 6, 2014 · (Imagine bringing the blue segment down so it lies on top of part of the purple segment - $\sin^2\theta + \cos^2\theta = 1$ (since $\sin^2\theta + \cos^2\theta = 1^2$). Since the radius has a length of $1$ and the total tangent segment (orange and turquoise combined) is perpendicular to the radius, this proves the other two Pythagorean ...

$$ \cos^2 i = {(b/a)^2 − (b/a)^2_{eos} \over 1 − (b/a)^2_{eos}} $$ All I need however is to determine ...

Can you give me the solution for the summation $$ \\sum_{n=0}^{\\infty} \\cos^2(\\pi n) $$ Edit: Please give me the explanation of how it is calculated and also final answer in integers.

Nov 23, 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.

I need to prove that $\cos(x)^2+\sin(x)^2=1$ Here's how I started (using the Cauchy product): \begin{align} \cos(x)^2+\sin(x)^2 &=\sum_{k=0}^{\infty}\sum_{l=0}^k ...