Express $Cosec \theta$ in terms of $tan \theta$

Given :

The given term is $ cosec \theta$.

To do :

We have to express $Cosec \theta$ in terms of $tan \theta$.

Solution:

$Cosec θ$ in terms of $tan θ$.

We know that,

$cosec^2 θ - cot^2 θ = 1$ and $cot θ = \frac{1}{tan θ}$

Therefore,

$cosec^2 θ - cot^2 θ = 1$ 

$cosec^2 θ = 1+cot^2 θ$

$cosec^2 θ = 1+ \frac{1}{tan^2 θ}$

$cosec^2 θ = \frac{tan^2 θ+1}{tan^2 θ}$

$cosec θ = \sqrt{\frac{tan^2 θ+1}{tan^2 θ}}$.

therefore, $Cosec θ$ in terms of $tan θ$ is $\sqrt{\frac{tan^2 θ+1}{tan^2 θ}}$.

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Updated on: 10-Oct-2022

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