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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1$\begingroup$ en.wikipedia.org/wiki/List_of_trigonometric_identities has a lot. If you want a more extensive list, I don't know. $\endgroup$– Eric TresslerSep 21, 2015 at 13:55
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$\begingroup$ there are only statement/identities but i seek parsing something like $$ \sin^2 \alpha + \cos^2 \alpha = 1 => b^2 + a^2 = c^2 => \frac{b^2}{c^2} + \frac{a^2}{c^2} = 1 $$ $\endgroup$– volkovSep 21, 2015 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.
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.
