Question

Let $\sec \theta =cosec\varphi$ for $\theta ,\varphi$ being acute then find the value of $cosec(\theta +\varphi )$.

Answer 1

Given,

$\sec \theta =cosec\varphi$

or, $\sec \theta =\sec ({90}^o-\varphi )$

or, $\theta +\varphi ={90}^o$. [ Since $\theta ,\varphi$ are acute]

Then,

$cosec(\theta +\varphi )$

$=cosec{90}^o$

$=1$.