# [P3D] EditVoicepack XL (5.5.15) SKIDROW

By: kaljai [P3D] EditVoicepack XL (5.5.15) SKIDROW

WORLD:
3b48bd18ac. 7 Oct 2018.

So there’s my information about whether or not i got my serial number, because the comfy thing is i want to go and update my game, but i’ll just see if that gets me a key.

A:

A more popular serial number finder is: Skidrow Serial Number

Q:

$\sqrt{1+2 \cos^2 \theta}=1+\cos \theta$

Show that $\sqrt{1+2 \cos^2 \theta}=1+\cos \theta$
I know the solution, but I have no idea why is this useful. I was given the following hint: If $x = 1+\cos \theta$, then $x^2 = 1+2 \cos^2 \theta$

A:

$$\sqrt {1+2\cos ^2 \theta } = \sqrt {(1+\cos \theta )(1+\cos \theta )} =$$
$$= (1+\cos \theta )\sqrt {1+\cos \theta } =$$
$$= (1+\cos \theta )(1+\cos \theta -\sin \theta ) =$$
$$= (1+\cos \theta )(1+\cos \theta +\cos \theta -\sin \theta ) =$$
$$= (1+2\cos ^2 \theta )+2\cos \theta$$
Here is what we got:
$$\sqrt {1+2\cos ^2 \theta } = 1+\cos \theta +\cos \theta -\sin \theta$$
So we just needed to prove that:
$$1+2\cos ^2 \theta = 2\cos \theta$$

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