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Find out everything you need to know before you buy IdeCAD Mimari 6 Full Version crack serial. Idecad Mimari 6 Crack Full VersionQ:
Is it true that $\frac{\cos(x)}{x}=\frac{\sin(x)}{x-\frac{\pi}{2}}$?
I was going through a paper and I faced this equality.
$\frac{\cos(x)}{x}=\frac{\sin(x)}{x-\frac{\pi}{2}}$
This was proved to be true by simply replacing $x$ by $kx$ and then dividing both the sides with $k$. This is fair but I was wondering if there is any neat way to prove it.
A:
Let $t=x-\frac{\pi}{2}$, so that $\frac{\cos x}{x} = \frac{\cos(x-\frac{\pi}{2})}{x-\frac{\pi}{2}} = \frac{\cos t}{t}$ and $\frac{\sin x}{x} = \frac{\sin(x-\frac{\pi}{2})}{x-\frac{\pi}{2}} = \frac{\sin t}{t}$. Then you can replace $t$ with $\frac{\pi}{2}-t$ and you have
$$
\frac{\cos(t)}{t} = \frac{\sin t}{t-\pi/2} = \frac{\sin t}{ -\pi/2 + t} = \frac{\cos t}{ -\pi/2 + t} = \frac{\cos t}{x} = \frac{\cos x}{x}.
$$
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