SOLUTION: Prove that: secx/sinx - sinx/cosx = cotx is an identity.

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Question 964790: Prove that:
secx/sinx - sinx/cosx = cotx is an identity.
Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
Prove that:
secx/sinx - sinx/cosx = cotx is an identity.
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secx/sinx - sinx/cosx = cotx
secx/sinx - sinx/cosx = cos/sin
1/sin*cos - sin/cos = cos/sin
Multiply by sin*cos
1 - sin^2 = cos^2
1 = sin^2 + cos^2 (Pythagorean Identity)
QED
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If anyone can post an example where working on one side only makes a difference, I would like to see it.

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Prove that:
secx/sinx - sinx/cosx = cotx is an identity.
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sec/sin - sin/cos = cos/sin
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Multiply thru by sin to get:
1/cos - sin^2/cos = cos
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Multiply thru by cos to get:
1 - sin^2 = cos^2
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cos^2 = cos^2
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Cheers,
Stan H.