Aspire Faculty ID #11121 · Topic: NIMCET 2022 · Just now
NIMCET 2022

If $cosec\theta-cot \theta=2$, then the value of $cosec\theta$ is

Solution

Given $\,\csc\theta-\cot\theta=2\,$ and the identity $\;(\csc\theta-\cot\theta)(\csc\theta+\cot\theta)=1\;$, we get $$\csc\theta+\cot\theta=\frac{1}{2}.$$ Adding the two equations: $$(\csc\theta-\cot\theta)+(\csc\theta+\cot\theta) $$ $$=2+\frac{1}{2}$$ $$\;\Rightarrow\;2\,\csc\theta=\frac{5}{2}.$$ Hence $$\csc\theta=\frac{5}{4}.$$

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