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Prove that : (sinx-sin3x)/(sin^(2)x-cos^...

Prove that : `(sinx-sin3x)/(sin^(2)x-cos^(2)x) = 2sinx`

Text Solution

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LHS` = (sinx-sin3x)/(sin^(2)x-cos^(2)x)`
`=((2cos(x+3x))/(2)sin(x-3x)/(2))/(-(cos^(2)x-sin^(2)x))`
`=(2cos2xsin(-x))/(-cos2x)`
`=(-2cos2xsinx)/(-cos2x)`
`(-2cos2xsinx)/(-cos2x)`
=2sinx = RHS Hence Proved.
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