Simplify the following trig expression

Question

 Simplify the following trig expression : 1/1-sec x - 1/1+sec x 

Answer 1

The LCD is  (1 - secx)(1 + secx).

 

 

Then the equivalent expression is

 

[(1 + secx) - (1 - secx)] / (1 - sec²x) =

 

2secx / (1 - sec²x)

 

 

Using the identity        1 + tan²x = sec²x

 

                                       tan²x = sec²x - 1

 

                                      -tan²x = 1 - sec²x

 

Obtain

 

-2sec²x / tan²x =

 

-2(1 / cos²x)(cos²x / sin²x) =

 

-2csc²x