## TRANSFORMATION FORMULAE

Formula to transform the product into sum or difference

The sine formula of the sum and difference of two angles is written as follows:

Add both the expression as follows:

Then, subtract expression (2) from expression (1) as follows:

Similarly consider the cosine formula of the sum and difference of two angles is written as follows:

Add both the expression as follows:

Then, subtract expression (3) from expression(4) as follows:

Therefore, following formula is obtained to transform the product into sum or difference

1.

2.

3.

4.

Formula to transform the sum or difference into product

Take the formula

Assume,

Then,

Substitute the values in the formulae obtained in transforming the product into sum or difference

1.

2.

3.

4.

Question 1

Write down the difference of as a product

Solution

Use the formula

Here, substitute the value in the formula as follows:

Question 2

Evaluate  using an appropriate product sum identity

Solution

Use the formula

Rewritten as follows:

Here, substitute the value in the formula as follows: