3(sinx-cosx)^4 + 4(sin^6x-cos^6x ) + 6(sinx + cosx )^2 = ????????

open 1st bracket make it into sin2x terms

2nd bracket make a²-b² open over cube then put expression for a³+b³ and a³-b³ to form cos2x and sin²2x terms

3rd bracket again make sin2x

finally we get sin²2x and cos2x terms

convert sin to cos to get cubic in cos2x

solve to get 13-8cos⁶x ans.......................