10-2

The sum and difference formula is to be explained only by using the formulas below:
tan (alpha+beta)= tan (alpha) + tan (beta)/ 1- tan (alpha) tan (beta).

the differnce formula for tangent is tan (alpha-beta)= tan (alpha) - tan (beta)/ 1+ tan (alpha) tan (beta).

The key to getting your solution is remembering to REPLACE. Here is an example.

Find tan (alpha + beta) and tan (alpha-beta)
Ex: tan (alpha)= 3/2 tan (beta)= 1/3

(3/2) + (1/3) / 1- (3/2) (1/3)
= (9/6) + (2/6) / 1- (3/6)
= (11/6) / (6/6)-(3/6)
= 11/6 / 3/6 = 11/3

(3/2)-(1/3) / 1+(3/2) (1/3)
= (9/6)-(2/6) / 1+ (3/2) (1/3)
=(7/6) / (6/6) + (3/6)
= 7/6 / 9/6 = 7/9

* slash (/) means divided by and represents a fraction

-Sameer