# Here is the expression: 2 ( sin 6 </msup> &#x2061;<!-- ⁡ --> x + cos

Here is the expression:
$2\left({\mathrm{sin}}^{6}x+{\mathrm{cos}}^{6}x\right)-3\left({\mathrm{sin}}^{4}x+{\mathrm{cos}}^{4}x\right)+1$
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1s1zubv
${\mathrm{sin}}^{4}x+{\mathrm{cos}}^{4}x=\left({\mathrm{sin}}^{2}x+{\mathrm{cos}}^{2}x{\right)}^{2}-2{\mathrm{sin}}^{2}x{\mathrm{cos}}^{2}x=1-2{\mathrm{sin}}^{2}x{\mathrm{cos}}^{2}x$
${\mathrm{sin}}^{6}x+{\mathrm{cos}}^{6}x=\left({\mathrm{sin}}^{2}x+{\mathrm{cos}}^{2}x{\right)}^{3}-3{\mathrm{sin}}^{2}x{\mathrm{cos}}^{2}x\left({\mathrm{sin}}^{2}x+{\mathrm{cos}}^{2}x\right)=1-3{\mathrm{sin}}^{2}x{\mathrm{cos}}^{2}x$
$2-6{\mathrm{sin}}^{2}x{\mathrm{cos}}^{2}x-3+6{\mathrm{sin}}^{2}x{\mathrm{cos}}^{2}x+1$
Which is 0, for all x

Desirae Washington
$2\left({\mathrm{sin}}^{6}x+{\mathrm{cos}}^{6}x\right)-3\left({\mathrm{sin}}^{4}x+{\mathrm{cos}}^{4}x\right)+1=$
$=2\left({\mathrm{sin}}^{2}x+{\mathrm{cos}}^{2}x\right)\left({\mathrm{sin}}^{4}x-{\mathrm{sin}}^{2}x{\mathrm{cos}}^{2}x+{\mathrm{cos}}^{4}x\right)-3\left({\mathrm{sin}}^{4}x+{\mathrm{cos}}^{4}x\right)+1=$
$=2\left({\mathrm{sin}}^{4}x-{\mathrm{sin}}^{2}x{\mathrm{cos}}^{2}x+{\mathrm{cos}}^{4}x\right)-3\left({\mathrm{sin}}^{4}x+{\mathrm{cos}}^{4}x\right)+1=$
$=-2{\mathrm{sin}}^{2}x{\mathrm{cos}}^{2}x-{\mathrm{sin}}^{4}x-{\mathrm{cos}}^{4}x+1=$
$-\left({\mathrm{sin}}^{2}x+{\mathrm{cos}}^{2}x{\right)}^{2}+1=-1+1=0$