SOLUTION: Can you please help me simplify this: (cosx)/(1-tanx) + (sinx*cosx)/(sinx-cosx)

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Question 1058747: Can you please help me simplify this:
(cosx)/(1-tanx) + (sinx*cosx)/(sinx-cosx)
Found 2 solutions by Alan3354, MathTherapy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
(cosx)/(1-tanx) + (sinx*cosx)/(sinx-cosx)
----
(cosx)/(1-tanx) + sinx/(tanx - 1)
- cosx/(tanx - 1) + sinx/(tanx - 1)
= (sin - cos)/(1 - tan) = (sin - cos)/(1 - sin/cos)
= (sin - cos)/((cos - sin)/cos)
= 1/(1/cos)
= cos(x)

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

Can you please help me simplify this:
(cosx)/(1-tanx) + (sinx*cosx)/(sinx-cosx)


 ------ Substituting matrix%281%2C3%2C+sin+%28x%29%2Fcos+%28x%29%2C+for%2C+tan+%28x%29%29

 ======>  

 ----- Applying KCF (KEEP, CHANGE, FLIP) to LEFT of "+"

 

 ------- Multiplying by LCD, - (cos x - sin x)

 ======>  ======> highlight%28highlight_green%28highlight%28cos+%28x%29%29%29%29