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