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Question
Prove the following result:
`tan^-1 1/7+tan^-1 1/13=tan^-1 2/9`
Solution
LHS = `tan^-1 1/7+tan^-1 1/13`
`=tan^-1((1/7+1/13)/(1-1/7xx1/13))` `[becausetan^-1x+tan^-1y=tan^-1((x+y)/(1-xy))`
`=tan^-1((20/91)/(90/91))`
`=tan^-1 2/9=` RHS
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