SOLUTION: sin(x+y)-2sinx+sin(x-y)/cos(x+y)-2cosx+cos(x-y)= tan x

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Question 151205: sin(x+y)-2sinx+sin(x-y)/cos(x+y)-2cosx+cos(x-y)= tan x
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!


We need these four identities to use on the left side:

sin%28x%2By%29=sin%28x%29cos%28y%29%2Bcos%28x%29sin%28y%29
sin%28x-y%29=sin%28x%29cos%28y%29-cos%28x%29sin%28y%29
cos%28x%2By%29=cos%28x%29cos%28y%29-sin%28x%29sin%28y%29
cos%28x-y%29=cos%28x%29cos%28y%29%2Bsin%28x%29sin%28y%29



Cancel positive and negative like terms
in numerator and in denominator:





Combine like terms:



Factor out 2sin%28x%29 in the top and 2cos%28x%29 in the
bottom:

2sin%28x%29%28cos%28y%29-1%29%2F%282cos%28x%29%28cos%28y%29-1%29%29=+tan%28x%29

Cancel the 2's and the %28cos%28y%29-1%29's.



sin%28x%29%2Fcos%28x%29=tan%28x%29

Then use identity sin%28x%29%2Fcos%28x%29=tan%28x%29

tan%28x%29=tan%28x%29

Edwin