How can we prove
$ sin (A^1 + A^2 + ... + A^n) = cos A^1 . cos (A^2) ... cos (A^n) [ S_1 - S_3 + S_5 ... ] $
where $S_n$ denotes sum of tangents of angles taken n at a time.
I tried proving it but failed. I can derive it easily for n = 2 and 3 but not for general case. Wikipedia has same kind of formula for tangent but it is not derived.
https://en.m.wikipedia.org/wiki/List_of_trigonometric_identities
Please give a very simple detailed proof.
Tuesday, 13 November 2018
trigonometry - How to prove this trigonometric identity of sine of n angles as sum?
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