Question 79

$$\sin^6 A + \cos^6 A$$ - 1 is equal to

Solution

sin6A + cos6A - 1

= (sin2A)3 + (cos2A)3 - 1

= (sin2A + cos2A)3 - 3sin2Acos2A(sin2A + cos2A) - 1 (∵ a3 + b3 = (a + b)3 - 3ab(a + b))

= (1)3 - 3sin2Acos2A × (1) - 1 (∵ sin2x + cos2x = 1)

= - 3sin2Acos2A

∴ sin6A + cos6A - 1 = - 3sin2Acos2A

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