Solve the following equations.
$c o s^{2} x + 5 c o s x = 2 s i n^{2} x .$

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Solution

${cos}^{2} x + 5 cos x = 2 {sin}^{2} x => {cos}^{2} x + 5 cos x = 2 - 2 {cos}^{2} x => 3 {cos}^{2} x + 5 cos x - 2 = 0 => 3 {cos}^{2} x + 6 cos x - cos x - 2 = 0 => 3 cos x (cos x + 2) - 1 (cos x + 2) = 0 ∴ cos x = \frac{1}{3} => x = 2 n π \pm {cos}^{- 1} \frac{1}{3}$
$cos x \neq - 2$ (no value of $x$ can ever yield the value $- 2$ )

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