Lösung 4.3:4d
Aus Online Mathematik Brückenkurs 1
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With the formula for double angles and the Pythagorean identity <math>\cos^2\!v + \sin^2\!v = 1</math>, we can express <math>\cos 2v</math> in terms of <math>\cos v</math>, | With the formula for double angles and the Pythagorean identity <math>\cos^2\!v + \sin^2\!v = 1</math>, we can express <math>\cos 2v</math> in terms of <math>\cos v</math>, | ||
| - | {{ | + | {{Abgesetzte Formel||<math>\begin{align} |
\cos 2v &= \cos^2\!v - \sin^2\!v\\[5pt] | \cos 2v &= \cos^2\!v - \sin^2\!v\\[5pt] | ||
&= \cos^2\!v - (1-\cos^2\!v)\\[5pt] | &= \cos^2\!v - (1-\cos^2\!v)\\[5pt] | ||
Version vom 08:55, 22. Okt. 2008
With the formula for double angles and the Pythagorean identity \displaystyle \cos^2\!v + \sin^2\!v = 1, we can express \displaystyle \cos 2v in terms of \displaystyle \cos v,
| \displaystyle \begin{align}
\cos 2v &= \cos^2\!v - \sin^2\!v\\[5pt] &= \cos^2\!v - (1-\cos^2\!v)\\[5pt] &= 2\cos^2\!v-1\\[5pt] &= 2b^2-1\,\textrm{.} \end{align} |
