Question : If the value of $\operatorname{cosec} A + \cot A = m$, then the value of $\operatorname{cosec} A - \cot A$ is:
Option 1: $\frac{1}m$
Option 2: $m$
Option 3: $\sqrt{m}$
Option 4: $m^2$
Correct Answer: $\frac{1}m$
Solution : Given: $\operatorname{cosec} A + \cot A = m$ We Know that, $\operatorname{cosec}^2 A - \cot^2 A = 1$ $⇒(\operatorname{cosec} A - \cot A)(\operatorname{cosec}A + \cot A) = 1$ Substituting $m$ for $\operatorname{cosec} A + \cot A$, we get: $\therefore\operatorname{cosec} A - \cot A = \frac{1}{m}$ Hence, the correct answer is $\frac{1}{m}$.
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