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  4. If cos -1((1/√5))=θ, then the value of cosec -1(√5) is

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Q. If $\cos ^{-1}\left(\frac{1}{\sqrt{5}}\right)=\theta$, then the value of $cosec\,{}^{-1}(\sqrt{5})$ is

Inverse Trigonometric Functions

Solution:

Let, $\cos ^{-1}\left(\frac{1}{\sqrt{5}}\right)=\theta $
$ \Rightarrow \cos \theta=\frac{1}{\sqrt{5}}$
$\Rightarrow \sec \theta=\sqrt{5} $
$\Rightarrow \sec ^{-1}(\sqrt{5})=\theta$
$\Rightarrow \frac{\pi}{2}-cosec\,{}^{-1}(\sqrt{5})=\theta $
$\Rightarrow cosec\,{}^{-1}(\sqrt{5})=\frac{\pi}{2}-\theta$