Prove that: a.) [csc^2(x)] * [tan^2(x)] -1 = [tan^2 (x)] b.) sec(x)/cos(x) - tan(x)/cot(x) = 1 show all your work for both the equations!

A.)

   

Use the identities  and  on the left-hand side

   

Make 1 have a common denominator to allow for fraction subtraction
Multiply the numerator and denominator of 1 by cos^2 x

   

Use Pythagorean identity for the numerator.

If  then subtracting both sides by  yields . We can substitute that into the numerator

   

======

b.)

   

For the left-hand side:
By definition,  and 

   

Since 

   

Using Pythagorean identity,  so