# Trigonometric equation: $$\displaystyle{2}{\left({{\sin}^{{6}}{x}}+{{\cos}^{{6}}{x}}\right)}-{3}{\left({{\sin}^{{4}}{x}}+{{\cos}^{{4}}{x}}\right)}+{1}={0}$$

Ean Hughes 2022-04-09 Answered
Trigonometric equation:
$2\left({\mathrm{sin}}^{6}x+{\mathrm{cos}}^{6}x\right)-3\left({\mathrm{sin}}^{4}x+{\mathrm{cos}}^{4}x\right)+1=0$
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Dallelopeelvep2yc
$2\left({\mathrm{sin}}^{6}x+{\mathrm{cos}}^{6}x\right)-3\left({\mathrm{sin}}^{4}x+{\mathrm{cos}}^{4}x\right)=0$

$2\left({t}^{6}+{\left(1-{t}^{2}\right)}^{3}\right)-3\left({t}^{4}+{\left(1-{t}^{2}\right)}^{2}\right)=0$
$2\left({t}^{6}+1-3{t}^{2}+3{t}^{4}-{t}^{6}\right)-3\left({t}^{4}+1-2{t}^{2}+{t}^{4}\right)=0$
$2\left(1-3{t}^{2}+3{t}^{4}\right)-3\left(2{t}^{4}+1-2{t}^{2}\right)=0$
$\left(2-6{t}^{2}+6{t}^{4}\right)-\left(6{t}^{4}+3-6{t}^{2}\right)=0$
$-1=0$