Kenneth S. answered • 04/17/17
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The left side is equal to (1-2sin2x)+sin2x which is 1-sin2x which is cos2x.
The right side is equal to ½(2sin x cos x)(cos x)/sin x which simplifies to cos2x.
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?--it's worthy of study and the key step uses the double angle sine formula.
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04/17/17
Kelsey D.
04/17/17