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$$ (|\cos A|)^2 \qquad\text{and}\qquad \cos^2 A $$

For example if $\cos A = 0.5$, and $0.5 \times 0.5 = 0.25$, are here some difference in the notations or are they equal?

Joonas Ilmavirta
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    They're the same. – Ashwath Rabindranath May 28 '15 at 21:11
  • If we lived in a perfect world $\cos^2(A)$ would mean $\cos(\cos(A))$ -- but we don't. –  May 28 '15 at 21:17
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    Notation is rarely perfect. But at least the convention of writing $\cos^2 A$ avoids all the extra characters and inelegance of $(\cos A)^2$ or $(|\cos A|)^2$. – Simon S May 28 '15 at 21:17
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    Consistent notation would require writing $(\cos A)^2$, but trigonometry has been developed when functions were not yet really used as nowadays. Since squares of sines and cosines appear very frequently in formulas, people started to used shorthands such as $\cos^2 A$ and now we're stuck with them. – egreg May 28 '15 at 21:37
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    Yet $cos^{-1}(x) \neq (cos(x))^{-1}$. It's all a mess really. – Jonathan Hebert May 28 '15 at 22:02

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