__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: