Question 871610: Prove: (sin3x/sinx)-(cos3x/cosx)=2
I cannot seem to figure this proof out. Please help!
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! Not sure if we are allowed to use the rather obscure identities
sin(3x) = 3sin(x) - 4sin^3(x)
cos(3x) = 4cos^3(x) - 3cos(x)
If not, you can derive them from sum and/or double angle formulas, e.g. sin(3x) = sin(2x+x)
From here, the proof is straightforward:
The first term becomes 3 - 4sin^2(x) after dividing by sin(x)
The second term becomes 3 - 4cos^2(x) after dividing by cos(x)
So we have 3 + 3 - 4(sin^2(x) + cos^2(x)) = 6 - 4 = 2
Done.
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