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# Product to Sum Trigonometry Identities Calculator

Enter the value of U & V, and select the term you want to find.

## Sum to Product Trigonometry Identities Calculator

Sum to Product Trigonometry Identities Calculator is used to simplify the trigonometric expression by sum to product trigonometric identities.

## What is meant by Sum to Product Trigonometry Identities?

The sum-to-product trigonometric identity is a formula that associates the sum or difference of two trigonometric functions with their product. These identities are found by solving the expression of addition and subtraction of trigonometric functions.

### Sum to Product Formulas:

Sin (U) + Sin (V) = 2 Sin [(U + V)/2] Cos [(U - V)/2]

Sin (U) - Sin (V) = 2 Sin [(U - V)/2] Cos [(U + V)/2]

Cos (U) - Cos (V) = -2 Sin [(U + V)/2] Sin [(U - V)/2]

Cos (U) + Cos (V) = 2 Cos [(U + V)/2] Cos [(U - V)/2]

## How to find the Sum to Product trigonometry identity value?

**Example 1:**

If angle one is 10 and angle two is 13 then find the solution of cosine sum identity.

**Solution:**

**Step 1:**

Write the data.

Angle one = U = 10, Angle two = V = 13, Cos (U) + Cos (V) =?

**Step 2: **

Write the formula of cosine sum to the product.

Cos (U) + Cos (V) = 2 Cos [(U + V)/2] Cos [(U - V)/2]

**Step 3:**

Put the value in the above formula and simplify.

U = 10, V = 13

Cos (10) + Cos (13) = 2 Cos [(10 + 13)/2] Cos [(10 - 13)/2]

Cos (10) + Cos (13) = 2 Cos [(23)/2] Cos [(-3)/2]

Cos (10) + Cos (13) = 2 Cos [11.5] Cos [-1.5]

Cos (10) + Cos (13) = 2 Cos [11.5] Cos [1.5]

Cos (10) + Cos (13) = 2 (0.9796)

**Cos (10) + Cos (13) = 1.9591**

**Example 2:**

If angle one is 9 and angle two is 13 then find the solution of sine sum identity.

**Solution:**

**Step 1:**

Write the data.

Angle one = U = 9, Angle two = V = 13, Sin (U) + Sin (V) =?

**Step 2: **

Write the formula of sine sum to the product.

Sin (U) + Sin (V) = 2 Sin [(U + V)/2] Cos [(U - V)/2]

**Step 3:**

Put the value in the above formula and simplify.

U = 9, V = 13

Sin (9) + Sin (13) = 2 Sin [(9 + 13)/2] Cos [(9 - 13)/2]

Sin (9) + Sin (13) = 2 Sin [(22)/2] Cos [(-4)/2]

Sin (9) + Sin (13) = 2 Sin [11] Cos [-2]

Sin (9) + Sin (13) = 2 Sin [11] Cos [2]

Sin (9) + Sin (13) = 2 (0.1907)

**Sin (9) + Sin (13) = 0.3814**