How to simplify cot2x/csc2x

Question

The goal is to simplify the trig indentity expression as much as possible using the different fundamentals of identities like reciprocal identities, quotient identities, and pythagorean identities

Answer 1

 Cot 2X  / CSC 2X =

 

   Cos 2x/ Sin2X  / 1/ Sin 2x =

 

    Cos 2X / Sin 2X  * Sin2X =

 

     Cos 2X =

 

     Cos ^2X - Sin^2 X

Answer 2

Rewrite both top and bottom as:      cot2x = cos2x/sin2x and 1/csc2x = sin2x

 

SO:       cot2x / csc2x  =          (cos2x/sin2x)(sin2x)          =     cos2x   

 

This last form is just the cosine of the double angle which is    = ANSWER =  cos²x - sin²x 

This answer is just one form of the cosine of the double angle.

There are others.