Sum of sines and cosines with arguments in arithmetic progression:

For any "a" and "b":

where arctan("y", "x") is the generalization of arctan("y"/"x") which covers the entire circular range (see also the account of this same identity in "symmetry, periodicity, and shifts" above for this generalization of arctan).

The above identity is sometimes convenient to know when thinking about the Gudermanian function.

If "x", "y", and "z" are the three angles of any triangle, i.e. if "x" + "y" + "z" = π, then

प्रयुक्त संकेतों (Notation) के बारे में
अनेक किन्तु सीमित पदों के योग की स्पर्शज्या
मौलिक सम्बन्ध
Other sums of trigonometric functions