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I understand simple trigonometric formulas like $ \sin^2 \alpha + \cos^2 \alpha = 1.$ I've found ones in books but I've not found more difficult like $$ \sin^2 \frac{\alpha}{2} = \frac{1 - \cos \alpha}{2} $$ or inverse trigonometric functions. Is there anywhere it?

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    $\begingroup$ en.wikipedia.org/wiki/List_of_trigonometric_identities has a lot. If you want a more extensive list, I don't know. $\endgroup$ – Eric Tressler Sep 21 '15 at 13:55
  • $\begingroup$ there are only statement/identities but i seek parsing something like $$ \sin^2 \alpha + \cos^2 \alpha = 1 => b^2 + a^2 = c^2 => \frac{b^2}{c^2} + \frac{a^2}{c^2} = 1 $$ $\endgroup$ – volkov Sep 21 '15 at 14:03
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Once you get past the introductory right angle approach to trigonometry, and identities such as Pythagorean and complimentary angle identities, you should start seeing that "trig" triangles and arbitrary $(a,b,c)$ triangles as all similar. enter image description here

After some practice, we only consider the "trig" triangles when doing proofs.

Later on, we take the unit circle approach, so that we can analyse and prove identities for angles larger than a quarter revolution, as well as negative angles.

To actually look up proofs, it may be productive to learn their names (e.g. Pythagorean identity, double angle formula, sum of angles formula, half angle formula, etc.), then just Google it.

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