Prove Trig Identity: CosθSinθ = Cos2θ+CosθSinθ

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SUMMARY

The discussion centers on the trigonometric identity involving Cosθ and Sinθ, specifically the equation \(\frac{CosθSinθ}{1 + Tanθ} = Cos2θ\). Participants conclude that this identity is a trick question, as it fails to hold true when substituting θ = 0, yielding 0 on the left side and 1 on the right. The correct approach is to solve the equation instead of proving the identity, identifying the solutions as the zeros of cosine, which are odd integer multiples of \(\pi/2\).

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Bradyns
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Prove:
\frac{CosθSinθ}{1 + Tanθ} = Cos2θ
===========================
I multiply out the denominator to get:

CosθSinθ = Cos2θ + CosθSinθ

I cannot seem to prove it.

Starting to think it's a trick question.. :/
 
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It most certainly is a trick question because the supposed identity doesn't even work if you plug in theta = 0. The left side is 0 while the right is 1, in this case!
 
You might be asked to solve the equation instead of proving the identity, and the solutions of the equation are the zeros of cosine, id est odd integer multiples of \pi/2.
 

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