First slide

Properties of ITF

Question

The principal value of ‘ $θ$ ’ for which $2 T a n^{- 1} (\cos θ) = T a n^{- 1} (2 \cos c e θ)$

Moderate

A

$\frac{π}{4}$
B

$\frac{π}{6}$
C

$\frac{π}{3}$
D

$\frac{π}{2}$

Solution

$W e h a v e 2 T a n^{- 1} (\cos θ) = T a n^{- 1} (2 \cos e c θ)$
$\begin{array}{l} \Rightarrow {Tan}^{- 1} (\frac{2 \cos θ}{1 - \cos^{2} θ}) = {Tan}^{- 1} (\frac{2}{\sin θ}) \\ \Rightarrow {Tan}^{- 1} (\frac{2 \cos θ}{1 - \cos^{2} θ}) = {Tan}^{- 1} (\frac{2}{\sin θ}) \\ \Rightarrow \frac{2 \cos θ}{\sin^{2} θ} = \frac{2}{\sin θ} \\ \Rightarrow \cot θ = 1 \\ \Rightarrow θ = \frac{π}{4} \end{array}$

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