functions - What is cos²(x)? - Mathematics Stack Exchange
Yes, $\cos^2 (x)$ usually means $\cos(x) \cdot \cos(x)$. Most other information already given here is also correct:
Prove $\\sin^2\\theta + \\cos^2\\theta = 1$ - Mathematics Stack …
Oct 6, 2014 · How do you prove the following: Pythagorean trigonometric identity. For all $\theta\in[0,2\pi]$ it holds that $$ \sin^2\theta+\cos^2\theta=1.$$ I'm curious to know of the different ways of provin...
Why $\cos^2 x-\sin^2 x = \cos 2x\;?$ - Mathematics Stack Exchange
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 ...
integration - Trigonometric Inequality $\cos 1 +\cos2+\ldots …
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trigonometry - Evaluating $\cos1°\cos2°\cos3°\cdots\cos89 ...
Feb 11, 2020 · $\begingroup$ Full disclosure, I didn't look any further into the suggestion I provided; I just happened to recall this being a usual "trick" for finding identities involving products of sines/cosines (case in point being the linked duplicate post).
Finding the general solution of $\\cos4 \\theta = \\cos2 \\theta
Jan 28, 2020 · You can solve it faster using congruences: $$\cos 4\theta=\cos2\iff4\theta\equiv\pm2\theta\mod 2\pi\iff2\theta,6\theta\equiv 0\mod2\pi\iff\begin{cases}\theta\equiv 0\mod\pi,\\[1ex]\theta\equiv 0\mod\dfrac\pi 3.\end{cases}$$ Now observe the first set of solutions is contained in the first, so that the set of solutions is …
How is $\\cos2\\theta = \\cos^2\\theta- \\sin^2\\theta$?
Mar 17, 2020 · On Khan Academy in this video at 3:53 minutes in, Khan uses the equation $\cos2\theta = \cos^2\theta- \sin^2\theta$, where can I view the proof for this statement? (He doesn't explain this part in that particular video)
$\\cos^2 \\alpha + \\cos^2 \\beta + \\cos^2 \\gamma =1$
Jun 27, 2019 · 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.
solution verification - Prove $\cos^2 (\theta)+\sin^2 (\theta) = 1 ...
Jun 7, 2021 · $\begingroup$ ""I can go from 1=1 to sin2(θ)+cos2(θ)=1 in a correct manner." That is true statement implies identity. That is not what you said. You said identity implies true statement. That is not a valid condition.
geometry - Prove that $\cos^2(\theta) + \cos^2(\theta …
Jul 18, 2015 · I am assuming that $\theta$ is in degrees. Then using the following formulas: \begin{eqnarray} \cos(x+y)&=&\cos x\cos y-\sin x\sin y\\ \cos(x-y)&=&\cos x\cos y+\sin x ...