## Sum To Product Formulas

In this page sum to product formulas we are going to see four formulas which are used frequently in trigonometry.

1.Sin C + Sin D = 2 Sin [(C+D)/2] cos [(C-D)/2]

2.Sin C - Sin D = 2 Cos [(C+D)/2] Sin [(C-D)/2]

3.Cos C + Cos D = 2 Cos [(C+D)/2] Cos [(C-D)/2]

4.Cos C - Cos D = 2 Sin [(C+D)/2] Sin [(C-D)/2]

Now we are going to see the example problems based on the above formulas.

Example 1:

Express Sin 4A + sin 2A in the form of product.

Solution:

Here the given question looks like Sin C + Sin D.So we have to use the formula

Sin C + Sin D = 2 Sin [(C+D)/2] cos [(C-D)/2]

Instead of C we have 4A and instead of D we have 2A.So we have to apply these values in the formula.

Sin 4A + sin 2A = 2 Sin [(4A+2A)/2] Cos [(4A-2A)/2]

=  2 Sin (6A/2) Cos (2A/2)

=  2 Sin 3A Cos A

Example 2:

Express Sin 5A - sin 3A in the form of product.

Solution:

Here the given question looks like Sin C - Sin D.So we have to use the formula

Sin C - Sin D = 2 Cos [(C+D)/2] Sin [(C-D)/2]

Instead of C we have 5A and instead of D we have 3A.So we have to apply these values in the formula.

Sin 5A - sin 3A = 2 Cos [(5A+3A)/2] Sin [(5A-3A)/2]

=  2 Sin (8A/2) Cos (2A/2)

=  2 Sin 4A Cos A

Example 3:

Express Cos 3A + Cos 7A in the form of product.

Solution:

Here the given question looks like Cos C+Cos D.So we have to use the formula

Cos C + Cos D = 2 Cos [(C+D)/2] Cos [(C-D)/2]

Instead of C we have 3A and instead of D we have 7A.So we have to apply these values in the formula.

Cos 3A + Cos 7A = 2 Cos [(3A+7A)/2] Cos [(3A-7A)/2]

=  2 Sin (10A/2) Cos (-4A/2)

=  2 Sin 5A Cos(-2A)

=  2 Sin 5A Cos 2A

Related Topics

Sum To Product Formulas to Trigonometry