Question

question attached above
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Answer 1

Answer:

Option 1

Step-by-step explanation:

Put x=tan alpha

So, arc tan x=alpha

Now,

$arc \: tan( \frac{1 - x}{1 + x} ) \\ = arc \: \tan( \frac{1 - \tan( \alpha ) }{1 + \tan( \alpha ) } ) \\ = arc \tan( \tan( 45 - \alpha ) ) = 45 - \alpha$

Now ,

$45 - \alpha = \frac{ \alpha }{2} \\ 3 \frac{ \alpha }{2} = 45 \\ 3 \alpha = 90 \\ \alpha = 30 \\ x = \tan( \alpha ) = \tan(30) = \frac{1}{ \sqrt{3} }$

The answer is option 1.

Thank you