Question

cos inverse(1-x^2/1+x^2)​

Answer 1

Step-by-step explanation:

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${cos}^{ - 1} ( \frac{1 - {x}^{2} }{1 + {x}^{2} } )$

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$\implies {cos}^{ - 1} (\frac{1 - {x}^{2} }{1 + {x}^{2} } ) \\ let \: x = \tan( \theta) \\ \implies {cos}^{ - 1} ( \frac{1 - {tan}^{2}( \theta) }{1 + {tan}^{2}( \theta) } ) \\ \implies {cos}^{ - 1} (cos (2 \theta)) \\ \implies 2( \theta) \\ \implies \boxed{ 2 \: {tan}^{ - 1} (x)}$