find x given that 9^(sin^2 x) +9^(cos^2 x) =2


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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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