Prove that `tan^-1(1/7)+tan^-1(1/13)=tan^-1(2/9)`

1.	Prove that `tan^-1(1/7)+tan^-1(1/13)=tan^-1(2/9)`
Answer» We know that `tan^(-1)x+tan^(-1)y=tan^(-1)(x+y)/(1-xy), xy lt 1`. Let `x=1/7` and `y=1/13`. Then, `xy=1/91 lt 1`. `therefore tan^(-1)1/7 +tan^(-1){(1/7+1/13)/(1-1/7 xx 1/13)}=tan^(-1)(20/90)=tan^(-1)2/9`.

Discussion

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