Answer
$\frac{cos~x-2}{cos^2x-4}=\frac{1}{cos~x+2}$
Work Step by Step
$\frac{cos~x-2}{cos^2x-4}=\frac{cos~x-2}{cos^2x-2^2}=\frac{cos~x-2}{(cos~x+2)(cos~x-2)}=\frac{1}{cos~x+2}$
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