SOLUTION: (2sinxcosx + cosx - 2sinx - 1)/(-sin(squared)x) = (2 sinx + 1)/(cosx+1) Please prove one side to equal the other (verify identity). Thank you.

Algebra ->  Trigonometry-basics -> SOLUTION: (2sinxcosx + cosx - 2sinx - 1)/(-sin(squared)x) = (2 sinx + 1)/(cosx+1) Please prove one side to equal the other (verify identity). Thank you.      Log On


   

Question 135374: (2sinxcosx + cosx - 2sinx - 1)/(-sin(squared)x) = (2 sinx + 1)/(cosx+1)
Please prove one side to equal the other (verify identity). Thank you.
Answer by kev82(151) About Me  (Show Source):
You can put this solution on YOUR website!
It's not exactly an identity as for x=0 the LHS is not evaluable but the RHS is. Similar for x=pi.
Let S=sin, C=cosine then the first thing I will do is multiply the whole thing by SS(C+1). This gives
-(C+1)(2SC+C-2S-1)=(2S+1)SS
expanding all the brackets gives
-(2SCC + CC - 2SC -C +2SC + C - 2S - 1) = 2SSS + SS
With some cancellations
-(2SCC + CC - 2S - 1) = 2SSS + SS
Now CC + SS =1, so CC = 1-SS, substituting this in gives
-(2S - 2SSS + 1 - SS - 2S - 1) = 2SSS + SS
From here it is just trivial cancellation to see that both are the same.