CBSE Class 10 Answered
sinA +cosA = x
Asked by | 10 Sep, 2012, 10:53: PM
Expert Answer
We know: a3 + b3 = (a + b)(a2 + b2 - ab)
=> sin6A + cos6A = (sin2A + cos2A)(sin4A + cos4A - sin2Acos2A)
= (sin2A + cos2A)2 - 3sin2Acos2A = 1 - 3(sinAcosA)2
As sinA + cosA = x
Squaring both sides
=> sin2A + cos2A + 2sinAcosA = x2
=> sinAcosA = (x2 - 1)/2
Therefore,
sin6A + cos6A = 1 - 3(sinAcosA)2 = 1 - 3(x2 - 1)2/4 = [4 - 3(x2 - 1)2]/4
Hence Proved.
Answered by | 11 Sep, 2012, 09:53: AM
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