Prove that : `sin^-1 (frac{5}{13}) + cos^-1 (frac{4}{5}) = frac{1}{2} sin^-1 (frac {3696}{4225})` .

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Prove that : sin^-1 frac{5}{13} + cos^-1 frac{3}{5}= tan^-1 frac{63}{16}

Prove that : sin^-1 frac{5}{13} + sin^-1 frac{7}{25}= cos^-1 frac{253}{325}

Prove that : sin^-1 (frac{3}{5}) + cos^-1 (frac{5}{sqrt26}) = tan^-1 (frac {19}{17}) .

Prove that : cos^-1 frac{12}{13} + sin^-1 frac{4}{5}= tan^-1 frac{63}{16}

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

Prove that : sin^-1 frac{3}{5} + sin^-1 frac{8}{17}= cos^-1 frac{36}{85}

tan^-1 frac{1}{2} + tan^-1 frac{2}{11}= frac{1}{2}sin^-1 frac{24}{25}

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

cos^-1 frac{12}{13}+ sin^-1 frac {3}{5}= sin^-1 frac{56}{65}

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