First slide

Introduction to ITF

Question

$If θ = \tan^{- 1} a, ϕ = \tan^{- 1} b and ab = - 1, then (θ - ϕ)$ is equal to

Moderate

A

0
B

$\frac{π}{4}$
C

$\frac{π}{2}$
D

None of these

Solution

$\begin{array}{l} Given that, θ = \tan^{- 1} a \\ and ϕ = \tan^{- 1} b \\ and ab = - 1 \end{array} \begin{array}{l} ∴ \tan θtan ϕ = ab = - 1 \\ \Rightarrow \tan θ = - \cot ϕ \\ \Rightarrow \tan θ = \tan (\frac{π}{2} + ϕ) \Rightarrow θ - ϕ = \frac{π}{2} \end{array}$

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