Question

Prove the following:

sin²6x − sin²4x = sin2x sin10x

Answer 1

L.H.S. = sin²6x − sin²4x 

= (sin6x + sin4x) (sin6x – sin4x)

= `2sin((6x + 4x)/2)*cos((6x - 4x)/2) xx 2cos((6x + 4x)/2)*sin((6x - 4x)/2)`

= 2sin5x · cosx × 2cos5x · sinx

= 2sin x cosx × 2sin5x · cos5x

= sin2x · sin10x

= R.H.S.