In the following problem, the expression is the right side of the formula for cos (alpha - beta) with particular values for alpha and beta. cos (79 degree) cos (19 degree) + sin (79 degree) sin (19 degree) Identify alpha and beta in each expression.
The value for alpha: degree
The value for beta: degree
Write the expression as the cosine of an angle. cos degree
Find the exact value of the expression. (Type an exact answer, using fraction, radicals and a rationalized denominator.)

1.     and

2.  

3.  

Step-by-step explanation:

Given

Solving for and

In trigonometry;

Equate the above expression to

and

By comparison

Compare expression on the right hand side to the left hand side

This implies that

By further comparison

and

Substitute and in

Hence, the expression is

Solving for the exact values;

Express as a difference of angles

Recall that

So;

------------------------------------------------------------------------------------

In trigonometry;

; ; ; ;

---------------------------------------------------------------------------

becomes

Hence;