How do you prove $tan^-1(1/4)+tan^-1(2/9)=tan^-1(1/2)$ ?

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Answer 1 · 2016-11-06T01:12:13

$LHS=tan^-1(1/4)+tan^-1(2/9)$

$=tan^-1((1/4+2/9)/(1-1/4xx2/9))$

$=tan^-1(((9*1+4*2)/36)/((36-2)/36))$

$=tan^-1((17/36)/((34)/36))$

$=tan^-1(cancel17/cancel36xxcancel36/cancel34^2)$

$=tan^-1(1/2)=RHS$

Proved

How do you prove tan^-1(1/4)+tan^-1(2/9)=tan^-1(1/2)tan^-1(1/4)+tan^-1(2/9)=tan^-1(1/2)?