Simplify ^@ \sqrt { \dfrac{ 1 + \cos \theta } { 1 - \cos \theta | Math Question and Answer | Edugain Indonesia

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Simplify $\sqrt { \dfrac{ 1 + \cos \theta } { 1 - \cos \theta } } + \sqrt { \dfrac{ 1 - \cos \theta } { 1 + \cos \theta } }$

Answer:

$2 cosec\theta$

Step by Step Explanation:

$\begin{align} & \sqrt { \dfrac{ (1 + \cos \theta)(1 + \cos \theta) } { (1 - \cos \theta)(1 + \cos \theta) } } + \sqrt { \dfrac{ (1 - \cos \theta)(1 - \cos \theta) } { (1 + \cos \theta)(1 - \cos \theta) } } \\ = & \sqrt { \dfrac{ (1 + \cos \theta)^2 } { \sin^2 \theta } } + \sqrt { \dfrac{ (1 - \cos \theta)^2 } { \sin^2 \theta } } \\ = & \dfrac{ (1 + \cos \theta + 1 - \cos \theta) } { \sin \theta } \\ = & 2 \mathrm{cosec} \theta \\ \end{align}$

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