- #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.

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- Thread starter Miike012
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- #1

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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.

- #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)

cos^2/(cos-sin) + sin^2/(sin-cos)

(cos^2 - Sin^2)/(cos-sin)

- #4

Dick

Science Advisor

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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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