For any two vectors `vecu and vecv` prove that `(1+|vecu|^2)(1+|vecv|^2) = (1-vecu.vecv)^2+|vecu+vecv+(vecuxxvecv)|^2`

Explanation

To prove the equation

\[ (1 + |\vec{u}|^2)(1 + |\vec{v}|^2) = (1 - \vec{u} \cdot \vec{v})^2 + |\vec{u} + \vec{v} + (\vec{u} \times \vec{v})|^2, \]

we will start by simplifying both sides of the equation step by step.

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