Sum of Squares of Sine and Cosine

Theorem
$$\cos^2 x + \sin^2 x = 1$$

Corollary

 * $$1 + \tan^2 x = \sec^2 x$$ (when $$\cos x \ne 1$$)


 * $$1 + \cot^2 x = \csc^2 x$$(when $$\sin x \ne 1$$)

Proof
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Corollary

 * $$1 + \tan^2 x = \sec^2 x$$ (when $$\cos x \ne 1$$):

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 * $$1 + \cot^2 x = \csc^2 x$$(when $$\sin x \ne 1$$):

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