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How would I verify the following trig identity?

$$(r\sin A \cos A)^2+(r\sin A \sin A)^2+(r\cos A)^2=r^2$$

My work thus far is

$$(r^2\cos^2A\sin^2A)+(r^2\sin^2A\sin^2A)+(r^2\cos^2A)$$

But how would I continue? My math skills fail me.

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    Sorry for not being able to type my post in mathjax I just lack the technical skill.2012-07-18
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    Look for common factors in each term of the expression. What do you get when you factor these out?2012-07-18
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    I think you lost a plus sign in there.2012-07-18
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    You can't solve for $r$, as $r^2$ is a common factor of your equation. If you assume $r \ne 0$ you can divide out the $r^2$. You can prove that it is an identity.2012-07-18

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