This document discusses proving trigonometric identities. It lists four common operations for proving identities: 1) adding or subtracting rational expressions, 2) multiplying or dividing rational expressions, 3) factoring, and 4) multiplying by the conjugate. It then provides four examples of identities to prove using these techniques.

1. Exercise #15
Trigonometric Identities II
When LHS = RHS, the identity has been proved. Some common operations when
proving identities are:
1. Adding/Subtracting rational expressions
1 1
Ex.  2
cos  sin 
2
2. Multiplying/Dividing rational expressions
 1  1 
Ex.   2 
 cos   sin  
2
3. Factoring
Ex. sin   sin  cos 
3 2
4. Multiplying by the conjugate
1
Ex.
1  sin 

2. Examples
Prove each of the following:
tan   cot 
1.  2sin 2   1
tan   cot 
2. cos   tan  sin   sec

3. 3. sin  cos sec csc  1
1  tan 2 
4.  csc2 
tan 
2