Question

Find the value of $\operatorname{cosec}\left\{\cot \left(\cot ^{-1} \frac{3 \pi}{4}\right)\right\}$.

Answer 1

SOLUTION :    $\because  \cot \left(\cot ^{-1} x\right)=x, \forall x \in R \\$

$\therefore \quad  \cot \left(\cot ^{-1} \frac{3 \pi}{4}\right)=\frac{3 \pi}{4} \\$

$ \operatorname{cosec}\left\{\cot \left(\cot ^{-1} \frac{3 \pi}{4}\right)\right\}=\operatorname{cosec}\left(\frac{3 \pi}{4}\right)=\sqrt{2} $