`cot^-1 frac {ab+1}{a-b} + cot^-1 frac {bc+1}{b-c} + cot^-1 frac {ca+1}{c-a}=0`

tan^-1 frac{1}{2} + tan^-1 frac {1}{7} = tan^-1 frac{9}{13}

tan^-1 frac{1}{2} + tan^-1 frac {2}{11} = tan^-1 frac{3}{4}

Show that : tan^-1 frac{1}{2} + tan^-1 frac{1}{4}=frac{1}{2} cos^-1 frac{13}{85}

Show that : tan^-1 frac{1}{2} + tan^-1 frac{1}{5}=frac{1}{2} cos^-1 frac{16}{65}

tan^-1 frac{1}{5} + tan^-1 frac{1}{7} + tan^-1 frac {1}{3} + tan^-1 frac{1}{8}= frac{pi}{4}

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

If cos^-1 frac {x}{a} + cos^-1 frac {y}{b}= alpha , prove that : frac {x^2}{a^2}- frac{2xy}{ab} cos alpha + frac {y^2}{b^2}= sin^2 alpha

Show that : tan^-1 frac{1}{3} + tan^-1 frac{1}{5}=frac{1}{2} cos^-1 frac{33}{65}

2tan^-1 frac{1}{3} + tan^-1 frac{1}{7}= frac {pi}{4}

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