Prasenjeet S.

asked • 07/03/14

How to Prove

Sin2 (6x) - Sin2 (4x) = sin(2x)Sin(10x)

1 Expert Answer

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Imtiazur S. answered • 07/03/14

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Use sin(2x)=sin(6x-4x) and sin(10x)=sin(6x+4x) and simplify to arrive at the expression on the left.  Very simple.
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Prasenjeet S.

Thanks!
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07/03/14

Imtiazur S.

tutor
f(x)2-f(y)2 is not always f(x-y)*f(x+y) although this is ALWAYS true in case of Sine function.  The proof is more involved than the proof I added above.  I apologize for the misleading answer I provided and for any trouble this caused the student for trusting the above proof.
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06/23/16

Imtiazur S.

tutor
On second look, my solution is not as bad as I thought it was.  Trigonometric insight and some algebra is all it takes to prove the identity.
 
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06/23/16

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