सिद्ध कीजिए - `(sin x -sin 3x)/(sin^(2)x - cos^(2)x)=2 sin x`.

Explanation

`L.H.S.=(sin x-sin 3x)/(sin^(2)x-cos^(2)x)`
`=(2sin ((x-3x)/(2))cos((x+3x)/(2)))/(-[cos^(2)x-sin^(2)x])`
`[because sin C - sin D = 2 "sin"(C-D)/(2)"cos"(C+D)/(2)]`
`rArr " " L.H.S. =(2sin(-x)cos(2x))/(-cos 2x) " " [because cos^(2)A - sin^(2)A=cos 2A]`
`=(-2sin x cos 2x)/(-cos 2x)`
`= 2sin x = R.H.S. " "` इति सिद्धम्