Question

If $\cot \theta =\frac{4}{3}$ and $\theta$ is acute then find, $2cosec\theta -4\sec \theta$.

Answer 1

$\cot \theta =\frac{4}{3}\frac{\cos \theta }{\sin \theta }=\frac{\frac{4}{5}}{\frac{3}{5}}\Rightarrow 2\csc \theta -4\sec \theta \Rightarrow \frac{2}{3}\times 5-\frac{4}{4}\times 5\Rightarrow \frac{10}{3}-\frac{20}{4}\Rightarrow \frac{40-60}{12}\Rightarrow \frac{-20}{12}\Rightarrow \frac{-5}{3}$