Prove the Trigonometric Identity

Question

-tan²x + sec²x = sec²xcos²x

Answer 1

Since the secx and cosx are reciprocals, the right side of the equation simplifies to 1.  

 

 

So, we just need to show that the left side of the equation also simplifies to 1:

 

-tan²x + sec²x = -sin²x/cos²x + 1/cos²x

 

                         = (1 - sin²x)/cos²x

 

                         = cos²x/cos²x

 

                         = 1