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Question

The general value of $x$ satisfying the equation $2 cot to the power of 2 end exponent invisible function application x plus 2 square root of 3 cot invisible function application x plus 4 blank c o s e c blank x plus 8 equals 0$ is

$n π - \frac{π}{6}, n \in Z$
$n π + \frac{π}{6}, n \in Z$
$2 n π - \frac{π}{6}, n \in Z$
$2 n π + \frac{π}{6}, n \in Z$

The correct answer is: $2 n pi minus fraction numerator pi over denominator 6 end fraction comma n element of Z$

$open parentheses cot invisible function application x plus square root of 3 close parentheses to the power of 2 end exponent plus cot to the power of 2 end exponent invisible function application x plus 4 blank c o s e c blank x plus 5 equals 0$
$rightwards double arrow open parentheses cot invisible function application x plus square root of 3 close parentheses to the power of 2 end exponent plus c o s e c to the power of 2 end exponent x plus 4 blank c o s e c blank x plus 4 equals 0 blank$
$rightwards double arrow open parentheses cot invisible function application x plus square root of 3 close parentheses to the power of 2 end exponent plus open parentheses c o s e c blank x plus 2 close parentheses to the power of 2 end exponent equals 0$
$rightwards double arrow cot invisible function application x equals negative square root of 3$ or $c o s e c blank x equals negative 2$
$rightwards double arrow x equals 2 n pi minus fraction numerator pi over denominator 6 end fraction comma n element of Z blank open parentheses because x element of 4 t h blank q u a d r a n t close parentheses$

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