# Product to Sum Calculator

Enter the values in the product to sum calculator and select the required operation.

## 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