Number of solution(s) of the equation $ln (2 - {sin}^{2} x) = 0$ where $x \in [0, 10 π]$ is

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Solution

$ln (2 - {sin}^{2} x) = 0$
$\Rightarrow 2 - {sin}^{2} x = 1$
$\Rightarrow {sin}^{2} x = 1 = {sin}^{2} \frac{π}{2}$
$\Rightarrow x = n π \pm \frac{π}{2}$
Now, $x \in [0, 10 π]$
$\Rightarrow x = \frac{π}{2}, \frac{3 π}{2}, \frac{5 π}{2}, \dots, \frac{19 π}{2}$
Number of solutions $= 10$

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