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`cos^(-1)((1-x^2)/(1+x^2))=....... ,(|x| le 1)`

If 0 le x lt oo, then cos^(-1)((1-x^(2))/(1+x^(2))) equals

If -oo lt x le 0 then cos ^(-1)((1-x^(2))/(1+x^(2))) equals

2 tan^(-1) x = sin^(-1) ((2x)/(1+x^(2))) , 1 le x le 1

Prove that: i) sin^(-1)(3x-4x^(3))=3sin^(-1)x, |x| le 1/2 ii) cos^(-1)(4x^(2)-3x)=3cos^(-1)x,1/2 le x le 1 iii) tan^(-1)""(3x-x^(3))/(1-3x^(2))=3tan^(-1)x, |x| lt 1/sqrt(3) iv) tan^(-1)x+tan^(-1)""(2x)/(1-x^(2))=tan^(-1)""(3x-x^(3))/(1-3x^(2))

Prove that sin^(-1) cos (sin^(-1) x) + cos^(-1) x) = (pi)/(2), |x| le 1

Prove that : sin^(-1)x+cos^(-1)x=(pi)/(2), |x| le 1

If |x| le 1 , then 2tan^(-1)x + sin^(-1)((2x)/(1+x^(2))) is equal to

Prove that : tan^(-1)((2xsqrt(1-x^(2)))/(1-2x^(2))) =2sin^(- 1)x when : - 1/(sqrt(2)) le x le 1/(sqrt(2))

Prove that sin^(-1) (2xsqrt(1-x^2))=2cos^(-1)x,1/sqrt2 le x le 1