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sin^(2)6x-sin^(2)4x=sin2xsin10x...

`sin^(2)6x-sin^(2)4x=sin2xsin10x`

Text Solution

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LHS `=sin^(2)6x-sin^(2)4x`
`=1/2[2sin^(2)6x-2sin^(2)4x]`
`=1/2[(1-cos12x)=(1-cos8x)]`
`[therefore 2sin^(2)nx=(1-cos2nx)]`
`=1/2[cos8x-cos12x]`
`1/2[2sin(8x+12x)/(2) sin(12x-8x)/(2)]`
`=sin10xsin2x=sin2xsin10x` =R.H.S.
Hence Proved.
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