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

  1. Trigonometric Ratios
  2. Trigonometric Identities
  3. Complementary Angles
  4. Values Of Certain Angles
  5. Heights And Distances
  6. Double Angle Formulas
  7. Half Angle Formulas
  8. Compound Angle Formulas
  9. 3A formulas
  10. Compound angles sum and differences
  11. Sum to product forms
  12. Trigonometry-Problems Using Identities
  13. Trigonometry Practical Problems





Sum To Product Formulas to Trigonometry