Question

$Ifcosec\theta +\cot \theta =m$ and $cosec\theta -\cot \theta =n$, prove that $mn=1$.

Answer 1

Given : $cosec\theta +\cot \theta =m$ and $cosec\theta -\cot \theta =n$

multiply both the equations we get,

$=(cosec\theta +\cot \theta )(cosec\theta -\cot \theta )$

$={cosec}^2\theta -{\cot }^2\theta$

$=1$......(As ${cosec}^2\theta -{\cot }^2\theta =1$)

$=mn$