Answer
$x=0$
Work Step by Step
$cos^2x+sin^2x=1$
$sin^2x=1-cos^2x$
$sin^2x+2cos~x=2$
$1-cos^2x+2cos~x-2=0$
$cos^2x-2~cos~x+2-1=0$
$cos^2x-2~cos~x+1=0$
$(cos~x-1)^2=0$
$cos~x-1=0$
$cos~x=1$
$x=0$
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