Verify the identity. 4 csc 2x = 2 csc2x tan x

Question

 Precalculus

 

Answer 1

They are NOT the same.

 

For a counterexample, Let x=pi/2

The left side is then 0

The right side is undefined.

 

Goto www.desmos.com and graph the functions;

  y = 4 csc2x and y = 2 csc2x tan x

They will NOT be the same graph

 

Finally, dividing both sides by 2 csc 2x in the given problem gives:

   2 = tan x which only happens at 63.435 degrees and 243.435 degrees