Trigonometry Sum to product and product to sum formulas or identities
Sum to product formulas for the tangent and the cotangent functions The product to sum formulas for the sine and cosine functions Trigonometric identities, examples
Sum to product formulas for the tangent and the cotangent functions
From the definition of the function tangent, or and and for the function cotangent or and Using the same method, and The product to sum formulas for the sine and cosine functions
By adding and subtracting addition formulas derived are following product to sum formulas, and  and Trigonometric identities examples
Example:   Use,  tan 45° = 1 and  tan 60° = Ö3,  to prove that  tan 15° = 2 - Ö3.
 Solution: Example:   Verify the identity Solution:   We divide the numerator and denominator on the left side by sin a and to the right side we use the cotangent formula for the difference of two angles, thus  Example:   Express tan 3x in terms of tan x.
Solution:   Using the sum formula and the double angle formula for the tangent function, Example:   Prove the identity Solution: Example:   Prove the identity Solution: Example:   If  tan a = 3/4, find tan a/2.
 Solution:   Use formula to express tan a/2  in terms of  tan a. Example:   Prove the identity Solution:   Substitute then Example:   Express the given difference  sin 61° - sin 59°  as a product.
 Solution:   Since  Example:   Prove the identity Solution:   Using the formula for the sum of the tangent     Trigonometry contents A 