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$$\sin^26x-\sin^24x=\sin2x\sin10x$$ Hi, Please help me to solve the above trigonometric function as i am trying to solve this question since last an hour.

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Its sin^2(6x)-sin^2(4x)=sin2xsin10x –  Drownpc Aug 29 '12 at 8:23
    
Thank you for your advice. –  Drownpc Aug 29 '12 at 8:27
    
... and (4) don't say "solve the trigonometric function". You solve equations, prove identitites, etc. You don't solve functions. –  Hans Lundmark Aug 29 '12 at 9:08
    
Is it a homework? If yes, please tagged with it. Sorry for me to ask a new "try to". –  vesszabo Aug 29 '12 at 13:34

1 Answer 1

$\sin^26x-\sin^24x=\sin(6x+4x)\sin(6x-4x)=\sin2x\sin10x$ applying $\sin^2A-\sin^2B=\sin(A+B)\sin(A-B)$

Alternatively,

$\sin^26x-\sin^24x=\frac{1}{2}(2\sin^26x-2\sin^24x)$ $=\frac{1}{2}(1-\cos12x-(1-\cos8x))$ as $\cos2A=1-2sin^2A$

So, $\sin^26x-\sin^24x=\frac{\cos8x-\cos12x}{2}=\sin10x\sin2x$ applying $\cos C - \cos D=-2\sin\frac{C+D}{2}\sin\frac{C-D}{2}=2\sin\frac{C+D}{2}\sin\frac{D-C}{2}$

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