solution:-
LHS = 2(sin6x + cos6x )- 3(sin4x + cos4x) + 1
{using this formula (a6 + b6)-click here & (a4 + b4)-click here}
2(sin2x + cos2x ){(sin2x + cos2x )2- 3(sin2x . cos2x)} -3{(sin2x + cos2x )2- 2 sin2x . cos2x } +1
2(1) {(1)2- 3(sin2x . cos2x)} -3{(1)2-2 sin2x . cos2x } +1
2(1- 3sin2x . cos2x)-3(1- 2 sin2x . cos2x ) +1
2 - 6sin2x . cos2x -3 + 6sin2x . cos2x +1
2-3+1
3-3
=0
=RHS proved
