Respuesta :
The required simplified expression is given as tan²(2x). Option c is correct.
[CSC(4x) - cot(4x) ] / [CSC(4x) + cot(4x) to be simplified.
What is simplification?
The process in mathematics to operate and interpret the function to make the function simple or more understandable called simplifying and the process is called simplification.
[tex]= [csc(4x) - cot(4x)] / [csc(4x) + cot(4x)] \\= [1/sin4x - cos4x/sin4x] / [1/sin4x + cos4x/sin4x]\\= [(1-cos4x)/sin4x] / [(1+cos4x) /sin4x] - - - - (1)[/tex]
Here,
[tex]1 - cos4x = 2sin^24x[/tex]
[tex]sin4x = 2sin2xcos2x,\\ 1+cos4x = 2cos^22x[/tex]
now put the value in equation 1
[tex]= [(2sin^22x)/2sin2xcos2x] / [(2cos^22x) /2sin2xcos2x] \\= [(sin2x)/cos2x] / [(cos2x) /sin2x] \\=tan2x/cot2x\\=tan^22x[/tex]
Thus, the required simplified expression is given as tan²(2x). Option c is correct.
Learn more about simplification here:
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