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Substitution Method to Remove Indeterminate Form

Solve the fol...

Question

Solve the following equations.
$l o g_{2} s i n x - l o g_{2} c o s x - l o g_{2} (1 - t a n x) - l o g_{2} (1 + t a n x) = 1.$

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Solution

it can be written as

${log}_{2} \frac{s i n x}{c o s x (1 - t a n x) (1 + t a n x)} = {log}_{2} \frac{s i n x}{c o s x (1 - {t a n x}^{2})}$

therefore

$\frac{t a n x}{1 - (t a n x)^{2}}$ =2

solving we get

tanx= $\frac{(17)^{1 / 2} - 1}{4}$

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