First slide

Properties of ITF

Question

$\tan (\frac{π}{4} + \frac{1}{2} \cos^{- 1} x) + \tan (\frac{π}{4} - \frac{1}{2} \cos^{- 1} x), x \neq 0$ is equal to

Easy

A

x
B

2x
C

2/x
D

none of these

Solution

Let cos^–1x = θ, then the given expression
$\begin{array}{l} = \frac{1 + \tan \frac{θ}{2}}{1 - \tan \frac{π}{2}} + \frac{1 + \tan \frac{θ}{2}}{1 + \tan \frac{θ}{2}} = \frac{2 (1 + \tan^{2} \frac{θ}{2})}{1 - \tan^{2} \frac{θ}{2}} \\ = \frac{2}{\cos θ} = \frac{2}{x} \end{array}$

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