यदि $\operatorname{cosec} \theta-\cot \theta=\frac{7}{2}$, $\operatorname{cosec} \theta$ का मूल्य

है:

$\operatorname{cosec} \theta-\cot \theta=\frac{7}{2}$

(i) $\operatorname{cosec}^{2} \theta-\cot ^{2} \theta=1$

$\Rightarrow \operatorname{cosec} \theta+\cot \theta=\frac{1}{\operatorname{cosec} \theta-\cot \theta}=\frac{2}{7} \ldots \ldots \text {..(ii) }$

On adding both equations,

$2 \operatorname{cosec} \theta=\frac{7}{2}+\frac{2}{7}$

$=\frac{49+4}{14}=\frac{53}{14} \Rightarrow \operatorname{cosec} \theta=\frac{53}{28}$