**Sum and Product formulas**

Some special angles like 30, 60, 90, 45, where trigonometric function has special values. (You can try them in the calculator, for decimal values, square it and you will know what it's like in surd form) For some angles like 15, 75, the trigonometric functions also have a special value, but it needs the formulae below to calculate.

**Sum of sine functions**

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**Sum of cosine functions:**

(Sorry, there is a typo: it should be sin alpha, but not cos alpha.)

**Sum of tangent functions:**

There are also some sum to product and product to sum formula. (The proof is now cancelled since it is obvious if you expand the R.H.S. of the formulae.)

Particularly, the sum to product formulae are all from the product to sum formulae. Using these formulas would be extremely useful and essential for integration of trigonometric functions.