Kenneth S. answered • 04/17/17

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The left side is equal to (1-2sin

^{2}x)+sin^{2}x which is 1-sin^{2}x which is cos^{2}x.The right side is equal to ½(2sin x cos x)(cos x)/sin x which simplifies to cos

^{2}x.Believe it!

Mark M.

While the two expressions are identical (as you aptly demonstrate), "proving an identity" requires that only one side (your choice) be converted.

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04/17/17

Kelsey D.

Proving identity states to work on one or both sides until they look the same.

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04/17/17

Kenneth S.

1. Kelsey, I like your comment that

*Proving identity states to work on one or both sides until they look the same.*This is certainly true because of

**the transitive property of equality (two quantities equal to a third quantity are equal to one another).**2. Mark M, I do of course recognize that conventional Trigonometry tours de force traditionally restrict the operations on a proposed identity to one side only, but in fact that is just a convention. (I was not willing to flail around to try to discover the transformation that would lead to the odde-looking right side.)

3. Kelsey, My work did show you how

*he right side equal cos2x?--i*t's worthy of study and the key step uses the double angle sine formula.
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04/17/17

Kelsey D.

^{2}x? When i simplify it down i get sin2x.04/17/17