सिद्ध कीजिए - `sin 2x+2sin 4x+sin 6x=4 cos^(2)x.sin 4x`

Explanation

`L.H.S. = sin 2x + 2 sin 4x + sin 6x`
`= 2sin (6x+2x)/(2)"cos"(6x-2x)/(2)+2 sin 4x`
`[because sin A + sin B = 2 sin ((A+B)/(2))cos((A-B)/(2))]`
`= 2sin 4x cos 2x + 2 sin 4x`
`= 2 sin 4x (cos 2x+1)`
`= 2sin 4x(2 cos^(2)x-1+1)`
`= 2 sin 4x.2cos^(2)x=4cos^(2)x sin 4x = R.H.S.` इति सिद्धम्