Simplify sec^2x + csc^2x / csc^2x(1+tan^2x)

Question

This is for my trig class. Thanks for the help!

Answer 1

 SEC ^2 X + CSC^2 X ( CSC^2 X ( 1 + Tan^2 X) =

 

   1            +     1        +     1                     =

COS ^2X      Sin^4 X      Sin^2X Cos ^2X

 

 

   Sin ^4 X               +   Cos ^2 X  + Sin^2 X =

  Sin ^4 X COS ^2 X      SIN^4 X COS^2 X

 

      SEC^2 X     +  SEC^2 x  . CSC ^4 x =

 

          SEC ^2 x ( 1 + CSC 4x )

Answer 2

sec²x + csc²x / csc²x(1+tan²x) = sec²x +1/(1+tan²x) = sec²x +1/sec² x = sec² x + cos² x