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Trig Identity

  • Thread starter Miike012
  • Start date
  • #1
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Homework Statement


Prove:
cosA/(1-tanA) + sinA/(1-cotA) = sinA + cosA


I have tryed turning tan and cot into sin and cos and everything but I can not prove it... can some one help??
Thank you.


Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
Dick
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Not until you show what you did that didn't work.
 
  • #3
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cos/(1-sin/cos)+ sin/(1-cos/sin)
cos^2/(cos-sin) + sin^2/(sin-cos)
(cos^2 - Sin^2)/(cos-sin)
 
  • #4
Dick
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cos/(1-sin/cos)+ sin/(1-cos/sin)
cos^2/(cos-sin) + sin^2/(sin-cos)
(cos^2 - Sin^2)/(cos-sin)
That's good! Now (cos^2-sin^2)=(cos-sin)*(cos+sin), right? Just multiply it out.
 
  • #5
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O wow, I dont know why I ddint notice that.... I think I have been studying to long ha...
 
  • #6
Mentallic
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cos/(1-sin/cos)+ sin/(1-cos/sin)
cos^2/(cos-sin) + sin^2/(sin-cos)
(cos^2 - Sin^2)/(cos-sin)
I'm very impressed! It hass been a long time since the precalculus forum has seen any consistently correct algebraic manipulations from a student in just 1 post!
 
  • #7
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Thank you... I just started doing them yesterday.
 

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