Simplify Sec^2x/cot^2x+1

Question

I'm trying to figure out how to simplify  this equation. 

Answer 1

 

Hi Janell,

 

sec²x/(cot²x+1) = sec²x/(cos²x/sin²x+1)     (as cotx = cosx/sinx)

 

                        = sec²x/((cos²x+sin²x)/sin²x)

 

                        = sec²x/(1/sin²x)               (as sin²x + cos²x = 1)

 

                        = sin²xsec²x

 

                        = sin²x/cos²x                     (as secx = 1/cosx)

 

                        = tan²x                            (as tanx = sinx/cosx)