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Question: If cos<sup>–1</sup>\(\frac{1–x^{2}}{1 + x^{2}}\) = 2tan<sup>–1</sup> x then x =...

If cos–11–x21+x2\frac{1–x^{2}}{1 + x^{2}} = 2tan–1 x then x =

A

xÎ R

B

|x| £ 1

C

x Î (–1, 1]

D

x Î [1, ¥)

Answer

x Î [1, ¥)

Explanation

Solution

p > 2tan–1x ³ 0 π2\frac{\pi}{2}> tan–1x ³ 0

also 1 + x2 ³ 1 – x2 ̃ x ³ 0