Find the number of solution of the equation $c o s^{2}$ x = 1 for which $x^{2} ⩽ 20.$

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Solution

$x^{2} \leq 20$
$(x - \sqrt{20}) (x + \sqrt{20}) \leq 0$
$x b e l o n g s t o (\sqrt{- 20}, \sqrt{20})$
Now, ${cos}^{2} x = 1$
$c o s x = 1$ $c o s = - 1$
$x = 0, 2 π, 4 π . . . . . .$ $x = π, 3 π, 5 π, . . . . . .$
combining we get x= $0, π, - π$

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