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

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


   

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) About Me  (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
:
%28-2sin2x%2Asinx%29%2F%282cos2x%2Asinx%29
:
%28-cross%282%29sin2x%2A+cross%28sinx%29%29%2F%28cross%282%29cos2x%2A+cross%28sinx%29%29
:
-sin%282x%29%2Fcos%282x%29
:
-tan2x remembering that sin/cos =tan