if-sinx-2-3-then-find-you-the-value-of-sin-6-x-cos-6-x-

Question Number 196639 by bbbbbbbb last updated on 29/Aug/23

if sinx = \frac{2}{3} then find you the value of \sin^{6} x + \cos^{6} x ? ? ?

Answered by AST last updated on 28/Aug/23

= {({s i n}^{2} x + {c o s}^{2} x)}^{3} - 3 {s i n}^{2} {c o s}^{2} x ({s i n}^{2} x + {c o s}^{2} x)

= 1 - 3 {s i n}^{2} (x) (1 - {s i n}^{2} x) (1) = 1 - 3 (\frac{4}{9}) (\frac{5}{9}) = \frac{7}{27}

Answered by Frix last updated on 28/Aug/23

s = \frac{2}{3}

c = \pm \sqrt{1 - s^{2}} = \pm \frac{\sqrt{5}}{3}

s^{6} + c^{6} = \frac{7}{27}

s^{6} + c^{6} = s^{6} + {(1 - s^{2})}^{3} = 3 s^{4} - 3 s^{2} + 1 = \frac{7}{27}

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