The value of cos⁡tan−1⁡tan⁡15π4, is - Infinity Learn by Sri Chaitanya

A
$\frac{1}{\sqrt{2}}$
B
$- \frac{1}{\sqrt{2}}$
C
1
D
none of these

Solution:

We have,

$\begin{array}{l} \cos \{\tan^{- 1} (\tan (\frac{15 π}{4}))\} \\ = \cos \{\tan^{- 1} (\tan (4 π - \frac{π}{4}))\} \\ = \cos \{\tan (\tan^{- 1} (- \frac{π}{4}))\} = \cos (- \frac{π}{4}) = \cos \frac{π}{4} = \frac{1}{\sqrt{2}} \end{array}$

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