Question

If $\sec \theta =\text{cosec}\varphi$ find the value of $\text{cosec}(\theta +\varphi )$.

Answer 1

Given,

$\Rightarrow$$\sec \theta =\text{cosec}\varphi$

$\Rightarrow$$\sec \theta =\sec (\frac{\pi }{2}-\varphi )$

$\Rightarrow$$\theta =\frac{\pi }{2}-\varphi$

$\Rightarrow$$\theta +\varphi =\frac{\pi }{2}$

$\Rightarrow$$\text{cosec}(\theta +\varphi )=1$........As $cosec\left(\frac{\pi }{2}\right)=1$