SOLUTION: can you show me the steps on how to change the trig identity of tanxcosx=cotx(secx-cosx) ?

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Question 285166: can you show me the steps on how to change the trig identity of tanxcosx=cotx(secx-cosx) ?
Found 2 solutions by stanbon, eggsarecool:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
change the trig identity of
tanxcosx = cotx(secx-cosx)
-------
tan*cos = [cos/sin][1/cos - cos]
------
tan*cos = [cos/sin][(1-cos^2)/cos]
-----
tan*cos = [cos/sin][sin^2/cos]
----
tan*cos = [cos/sin][sin/cos][sin]
---
tan*cos = [sin/cos][cos/sin][sin]
----
tan*cos = [tan(x)][cos]
================================
Cheers,
Stan H.
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Answer by eggsarecool(46) About Me  (Show Source):
You can put this solution on YOUR website!
Ok so lets rewrite everything in terms of sin%28x%29 and cos%28x%29
So we have
Multiply everything out.
sin%28x%29=%281%2Fsin%28x%29%29-%28cos%28x%29%29%5E2%2Fsin%28x%29 common denominator of sin%28x%29 on the right.
sin%28x%29=%281-%28cos%28x%29%29%5E2%29%2Fsin%28x%29 we know that 1-%28cos%28x%29%29%5E2=%28sin%28x%29%29%5E2
So sin%28x%29=%28sin%28x%29%29%5E2%2Fsin%28x%29
sin%28x%29=sin%28x%29