SOLUTION: Simplify to a single trig function: (cos3x-cosx)/(sin3x-sinx). PLEASE HELP ME, I DONT KNOW WHAT TO DO!!!!

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Question 181020: Simplify to a single trig function: (cos3x-cosx)/(sin3x-sinx). PLEASE HELP ME, I DONT KNOW WHAT TO DO!!!!
Answer by Mathtut(3670)   (Show Source): You can put this solution on YOUR website!
ok lets take the numerator first
:
these are just addition formulas we are using here: you have to have these formulas in your textbook:
:
cos3x-cosx=-2sin((3x+x)/2)sin((3x-x)/2)=-2 sin2x sinx
:
now for the denominator:
:
sin3x-sinx=2cos((3x+x)/2)sin((3x-x)/2)=2cos2x sinx
:
now lets put it all together
:

:

:

:
remembering that sin/cos =tan

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