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Prove that cos^(-1)((1-x^(2n))/(1+x^(2n)...

Prove that `cos^(-1)((1-x^(2n))/(1+x^(2n)))=2tan^(-1)x^n ,0 lt x llt oo`

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Since `0 lt x lt oo, 0 lt x^(n) lt oo`
Let `x^(n) = tan theta rArr theta in (0, pi//2)`
`cos^(-1) ((1 - x^(2n))/(1 + x^(2n))) = cos^(-1) ((1 - tan^(2) theta)/(1 + tan^(2) theta))`
`= cos^(-1) (cos 2 theta)`
`= 2 theta " " [:' theta in (0, pi)]`
`= 2 tan^(-1) x^(n)`
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CENGAGE PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
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