show that 6(sinx+cosx)p4+12(sinx-cosx)p2+8(sinp6x+cosp6x)=26 where p4,p2,p6are use for power4,power2(square),power6

Asked by  | 24th Aug, 2012, 03:37: PM

Expert Answer:

6(sinx+cosx)4+12(sinx-cosx)2+8(sin6x+cos6x)
= 6(sin2x+cos2x+2sinxcosx)2+12(sin2x+cos2x-2sinxcosx)+8(sin2x+cos2x)3 - 24sin2xcos2x(sin2x+cos2x)
= 6(1+2sinxcosx)2+12(1-2sinxcosx)+8 -24sin2xcos2x
= 6(1+4sin2xcos2x+4sinxcosx)+12(1-2sinxcosx)+8 -24sin2xcos2x
= 6+24sin2xcos2x+24sinxcosx+12-24sinxcosx+8 -24sin2xcos2x
= 26
 
Hence, proved.

Answered by  | 26th Aug, 2012, 11:28: PM

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