Contents

Basic Identities

Second Degree Identities

Simple Equations

Second Degree Equations

Quiz 

Trigonometry Main Page

Second Degree Identities

We can obtain 2 more identities by dividing sin² q + cos² q = 1 by cos² q  and sin q respectively.

but = tan q  and = sec q 

Therefore, tan² q + 1 = sec²q 

Similarly, by dividing the original identity by sin² q , we obtain:

1 + cot² q  = cosec²q 

These identities will be found useful in solving equations.

Example 1

Simplify (sec q  - tan q  )(sec q  + tan q  ) and deduce the value of sec q  + tan q  if sec q  - tan q  = 3

(sec q  - tan q  )(sec q  + tan q  ) = sec² q  - tan² q

                                                  = (1 + tan² q) - tan² q

                                                   = 1

sec q + tan q = =1/3

Example 2

Simplify