# PROVing trigonometry indenties

1. Sep 26, 2010

### ytx123

1. The problem statement, all variables and given/known data
(tanx - cosecx)2 - (cotx - secx)2 = 2(cosecx - secx)

2. Relevant equations
tanx = sinx/cosx
cotx = 1/tanx = cosx/sinx
cosecx = 1/sinx
secx = 1/cosx

3. The attempt at a solution

LHS = (tanx-cosecx)(tanx-cosecx) - (cotx-secx)(cotx-secx)
= tan2x - tanxcosecx - tanxcosecx + cosec2x - cot2x + cotxsecx + cotxsecx
= sin2x/cos2x - (sinx/cosx)(1/sinx) - (sinx/cosx)(1/sinx) + 1/sin2x - cos2x/sin2x + (cosx/sinx)(1/cosx) + (cosx/sinx)(1/cosx) - (1/cos2x)
= sin2x/cos2x - 2sinx/sinxcosx + 1/sin2x - cos2x/sin2x + 2cosx/sinxcosx - 1/cos2x
= sin2x-1 / cos2x + 1 - cos2x / sin2x - 2sinx+2cosx/sinxcosx
= -1 + 1 - 2sinx+2cosx / sinxcosx
= 2sinx + 2cosx / sinxcosx

and i'm stucked
help thanks in advance :)
ps. if i post in the wrong place im sry cos im new :/

2. Sep 26, 2010

### fzero

You need to use parentheses to clarify addition vs division to avoid making trivial mistakes. You missed a minus sign that's present in the part I bolded. With the correct signs in the last line, you can divide through to obtain the desired result.

3. Sep 26, 2010

### ytx123

oh! thanks for pointing out my mistake , i've got the answer already :D thanks

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