**Sum To Product Formulas**

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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**

**Trigonometric Ratios****Trigonometric Identities****Complementary Angles**

**Values Of Certain Angles****Heights And Distances****Double Angle Formulas****Half Angle Formulas****Compound Angle Formulas****3A formulas****Compound angles sum and differences****Sum to product forms****Trigonometry-Problems Using Identities****Trigonometry Practical Problems**

Sum To Product Formulas to Trigonometry