First slide

Properties of ITF

Question

$\cos \{\tan^{- 1} [\sin (\cot^{- 1} \sqrt{3})]\}$ is equal to

Moderate

A

$\frac{4}{\sqrt{5}}$
B

$\frac{2}{\sqrt{5}}$
C

$- \frac{2}{\sqrt{5}}$
D

none of these

Solution

$\cos \{\tan^{- 1} [\sin (\cot^{- 1} \sqrt{3})]\}$
$\begin{array}{l} = \cos |\tan^{- 1} (\sin \frac{π}{6})| = \cos (\tan^{- 1} \frac{1}{2}) \\ = \cos θ, where θ = \tan^{- 1} \frac{1}{2} (\tan θ = \frac{1}{2} \Rightarrow \cos θ = \frac{2}{\sqrt{5}}) \\ = \frac{2}{\sqrt{5}} \end{array}$

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