Sum to Product Trigonometry Identities Calculator

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