please..... prove the following

Asked by sunil_0010 | 1st Nov, 2009, 03:57: PM

Expert Answer:

a3+b3 = (a+b)(a2-ab+b2)

sin6A+cos6A = (sin2A)3+(cos2A)3 = (sin2A+cos2A)(sin4A - sin2Acos2A + cos4A)

              =(sin4A - sin2Acos2A + cos4A)

Using this,

2(sin6A+cos6A) - 3(sin4A+cos4A)+1 =

2(sin4A - sin2Acos2A + cos4A) - 3(sin4A+cos4A)+1 =

-2sin2Acos2A - sin4A - cos4A +1 =

-(sin4A + cos4A + 2sin2Acos2A) + 1 =

- (sin2A + cos2A)2 +1 =

-1 + 1 = 0

Regards,

Team,

TopperLearning.

Answered by  | 1st Nov, 2009, 10:52: PM

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