First slide

Trigonometric equations

Question

The number of distant solutions of the equation, $\log_{\frac{1}{2}} |\sin x| = 2 - \log_{\frac{1}{2}} |\cos x|$ in the interval , $[0, 2 π]$ is______________

Moderate

Solution

$\begin{array}{l} \log_{1 / 2} | \sin x | = 2 - \log_{1 / 2} | \cos x | \\ \log_{1 / 2} | \sin x \cos x | = 2 \\ | \sin x \cos x | = \frac{1}{4} \end{array}$
$\sin 2 x = \pm \frac{1}{2}, 2 x \in [0, 4 π]$

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