find-x-given-that-9-sin-2-x-9-cos-2-x-2-

Question Number 60814 by Forkum Michael Choungong last updated on 26/May/19

f i n d x g i v e n t h a t

9^{{s i n}^{2} x} + 9^{{c o s}^{2} x} = 2

Answered by $@ty@m last updated on 26/May/19

9^{y} + 9^{1 - y} = 2

9^{y} + \frac{9}{9^{y}} = 2

z + \frac{9}{z} = 2

z^{2} - 2 z + 9 = 0

z = \frac{2 \pm \sqrt{4 - 36}}{2}

z = \frac{2 \pm 4 \sqrt{2} i}{2}

z = 1 \pm 2 \sqrt{2} i

9^{\sin^{2} x} = 1 \pm 2 \sqrt{2} i

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