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Question

f $c o s e c blank theta minus cot invisible function application theta equals q comma blank$ then the value of $c o s e c blank theta$ is

$q + \frac{1}{q}$
$q - \frac{1}{q}$
$\frac{1}{2} (q + \frac{1}{q})$
None of these

The correct answer is: $fraction numerator 1 over denominator 2 end fraction open parentheses q plus fraction numerator 1 over denominator q end fraction close parentheses$

$c o s e c blank theta minus cot invisible function application theta equals q$
$therefore c o s e c blank theta blank plus cot invisible function application theta equals fraction numerator 1 over denominator q end fraction$
$therefore c o s e c blank theta equals fraction numerator 1 over denominator 2 end fraction open square brackets q plus open parentheses 1 divided by q close parentheses close square brackets blank$ (on addition)

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