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Maths-

General

Easy

Question

The solution set of $left parenthesis 5 plus 4 c o s invisible function application theta right parenthesis left parenthesis 2 c o s invisible function application theta plus 1 right parenthesis equals 0$ in the interval $left square bracket 02 pi right square bracket$ is

$\{\frac{π}{3}, \frac{2 π}{3}\}$
$\{\frac{π}{3}, π\}$
$\{\frac{2 π}{3}, \frac{4 π}{3}\}$
$\{\frac{2 π}{3}, \frac{5 π}{3}\}$

The correct answer is: $open curly brackets fraction numerator 2 pi over denominator 3 end fraction comma fraction numerator 4 pi over denominator 3 end fraction close curly brackets$

$open parentheses 5 plus 4 cos invisible function application theta close parentheses open parentheses 2 cos invisible function application theta plus 1 close parentheses equals 0$
$c o s invisible function application theta equals fraction numerator negative 5 over denominator 4 end fraction comma text which is not possible. end text$
$text Therefore, end text 2 c o s invisible function application theta plus 1 equals 0 rightwards double arrow c o s invisible function application theta equals negative fraction numerator 1 over denominator 2 end fraction rightwards double arrow theta equals fraction numerator 2 pi over denominator 3 end fraction comma fraction numerator 4 pi over denominator 3 end fraction$
$text The solution set is end text open curly brackets fraction numerator 2 pi over denominator 3 end fraction comma fraction numerator 4 pi over denominator 3 end fraction close curly brackets subset of left square bracket 02 pi right square bracket$

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