Find the sum of the values of $∠ A$ (in degrees), if
$2 {cos}^{2} A - 3 cos A + 1 = 0$

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Solution

$2 c o s^{2} A - 3 c o s A + 1 = 0$
$2 c o s^{2} A - 2 c o s A - c o s A + 1 = 0$
$2 c o s A (c o s A - 1) - 1 (c o s A - 1) = 0$
$(2 c o s A - 1) (c o s A - 1) = 0$
Either $2 c o s A - 1 = 0$ or $c o s A - 1 = 0$
$c o s A = \frac{1}{2}$ or $c o s A = 1$
$c o s A = c o s 60$ or $c o s A = c o s 0$
thus, $A = 60^{\circ}, 0^{\circ}$

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