Product to Sum Calculator

Product to Sum Calculator 

Product to sum identities calculator is used to rewrite and evaluate the trigonometric functions using power reduction formulas. This calculator requires the values of angles only.

What is the product to sum of trigonometric identities?

Product to sum or sum to product is a solution process used in trigonometry for convenience in computing. 

It allows multiplying two trigonometric values by a formula that uses addition and subtraction. 

The power reduction formulas are obtained by solving the second and third versions of the cosine double-angle formula.

Product to sum formulas:

• Sin(u)Sin(v) = 1/2 [ cos(u-v) - cos(u+v)]
• Cos(u)Cos(v) = 1/2 [ cos(u-v) + cos(u+v)]
• Sin(u)Cos(v) = 1/2 [ sin(u+v) + sin(u-v)]
• Cos(u)Sin(v) = 1/2 [ sin(u+v) - sin(u-v)]

How to find the sum to product of trigonometric identities?

Example:

Find Cos(u)Cos(v) for angels u=60 and v=30 degrees.

Solution:

= ½ [ cos(u-v) + cos(u+v)]

= ½ [cos (60-30) + cos (60+30)]

= ½ [ cos (30) + cos (90)]

= ½ (0.866)

= 0.43301