1. Tardigrade
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  4. cos ( cot -1( textcosec( cos -1 a)))= (where 0 < a < 1 )

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Q. $\cos \left(\cot ^{-1}\left(\text{cosec}\left(\cos ^{-1} a\right)\right)\right)=$ ______(where $0 < a < 1 )$

Gujarat CETGujarat CET 2019

Solution:

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Let $\cos ^{-1} a=\theta \Rightarrow \cos \theta=a $
$\Rightarrow \text{cosec} \,\theta=\frac{1}{\sqrt{1-a^{2}}}$
$\cos \left(\cot ^{-1}\left(\frac{1}{\sqrt{1-a^{2}}}\right)\right) $
Let $ \cot ^{-1} \frac{1}{\sqrt{1-a^{2}}}=\phi $
$\Rightarrow \cot \phi=\frac{1}{\sqrt{1-a^{2}}} $
$\Rightarrow \cos \phi=\frac{1}{\sqrt{2-a^{2}}}$