Coupon Accepted Successfully!


Transformation of a Product of Trigonometric Functions into a Sum or Difference

1. Let us find by expanding them by known formulae

So the above formula reduces to

 (Sum) (Product)

Thus a sum can be changed to a product or a product can be changed to a sum or difference. With the same procedure, we get.

  • Working Rule for changing product sum or difference
Example 1:
Express 2sin 4θ cos 2θ as a sum or difference

(1) Formula used is either (1) or (2) since both have sin and cos
(2) 4θ > 2θ

Note:- If the angle for the cosine function is bigger, use the formula (2).

Example 2:
Express as a sum or difference

Note: There is no formulae connecting cos and sin in this series.
Either change cos sin (or) sin cos

Sum reduces to sin 55° + sin 72° (cos 35° = sin 55°)
Now use formula (1)

The sum could be done by writing it as cos 35° + cos18° also.
The two answers may look different; but they are equivalent

Example 3:
Prove that

are supplementary angles

Try these:
1. Prove that
2. Prove that

Example 4:
If A + B + C = π , prove that sin 2A + sin 2B + sin 2C = 4 sin A sin B sin C

Test Your Skills Now!
Take a Quiz now
Reviewer Name