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Prove that: sin{tan^(-1)((1-x^2)/(2x))...

Prove that: `sin{tan^(-1)((1-x^2)/(2x))+cos^(-1)((1-x^2)/(1+x^2))}=1`

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If 0lexle1 then sin{tan^(-1)((1-x^(2))/(2x))+cos^(-1)((1-x^(2))/(1+x^(2)))} is equal to

If -1lexle0 then sin{tan^(-1)((1-x^(2))/(2x))-cos^(-1)((1-x^(2))/(1+x^(2)))} is equal to

If 0lexle1 then sin{tan^(-1)((1-x^(2))/(2x))+cos^(-1)((1-x^(2))/(1+x^(2)))} is equal to

If -1lexle0 then sin{tan^(-1)((1-x^(2))/(2x))-cos^(-1)((1-x^(2))/(1+x^(2)))} is equal to

Prove that 2tan^(-1)((1+x)/(1-x))+sin^(-1)((1-x^(2))/(1+x^(2)))=pi

Prove that sin[Cot^(-1) (2x)/(1-x^2)+Cos^(-1)((1-x^(2))/(1+x^(2)))]=1 .

Prove that sin^(-1)((2x)/(1+x^2))=tan^(-1)((2x)/(1-x^2))

Prove that sin^(-1)((2x)/(1+x^2))=tan^(-1)((2x)/(1-x^2))

Prove that : tan^(-1) ((sqrt(1-x^(2)))/(1+x)) = 1/2 cos^(-1) x

Prove that tan^(-1)((sqrt(1-x^(2)))/(1+x))=(1)/(2)cos^(-1)x