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Prove that : tan^-1 [frac { (1+z)^(1/2) ...

Prove that : `tan^-1 [frac { (1+z)^(1/2) - (1-z)^(1/2)}{ (1+z)^(1/2) + (1-z)^(1/2)}]=frac{pi}{4}-frac{1}{2} cos^-1 (z)`.

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Prove that : tan^-1 [frac { (1+x)^(1/2) - (1-x)^(1/2)}{ (1+x)^(1/2) + (1-x)^(1/2)}]=frac{pi}{4}-frac{1}{2} cos^-1x .

Prove that : 1+tan A tan frac (A)(2)= secA= tanA cot frac (A)(2)-1

Prove that : tan^-1[(sqrt(1+z) + sqrt(1-z))/(sqrt(1+z) - sqrt(1-z))= pi/4 + 1/2 cos^-1z

tan^-1 frac{2}{11} + tan^-1 frac{7}{24}= frac{1}{2}cos^-1 frac{3}{5}

Prove that : 2 tan^-1 frac{1}{5} + tan^-1 frac{1}{8}= tan^-1 frac{4}{7}

tan^-1 frac{2}{11} + tan^-1 frac {7}{24} = tan^-1 frac{1}{2}

Prove that : 2 tan^-1 frac{1}{5} + tan^-1 frac{1}{4}= tan^-1 frac{32}{43}

Prove that : 2 tan^-1 frac{1}{7} + tan^-1 frac{1}{3}=tan^-1 frac{9}{13}

Prove that : sin^2 frac (pi)(6)+ cos^2 frac(pi)(3)- tan^2 frac(pi)(4)=-1/2 .

Prove that : 2 tan^-1 frac{1}{2} + tan^-1 frac{1}{7}=tan^-1 frac{31}{17}