First slide

Properties of ITF

Question

The value of $\cos \{\tan^{- 1} (\tan \frac{15 π}{4})\}$ , is

Moderate

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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