Question

sin6theta+cos6theta+3sin2theta=1

Answer 1

Consider, sin6ө + cos6ө =1-3sin2өcos2ө(sin2ө)3 + (cos2ө)3 = (sin2ө + cos2ө)3 − 3 (sin2ө cos2ө)(sin2ө + cos2ө)   [since a + b = (a+b)3 − 3ab(a+b)]                            = 1 − 3sin2өcos2ө    [Since sin2ө + cos2ө = 1]

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