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Question
Prove that:
`tan^(-1)""1/5+tan^(-1)""1/7+tan^(-1)""1/3+tan^(-1)""1/8=pi/4`
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Solution
LHS:
`(tan^(-1)""1/5+tan^(-1)""1/7)+(tan^(-1)""1/3+tan^(-1)""1/8)`
`=tan^(-1)((1/5+1/7)/(1-1/5xx1/7))+tan^(-1)((1/3+1/8)/(1-1/3xx1/8)) [:.tan^(-1)A+tan^(-1)B=tan^(-1)((A+B)/(1-AB))] `
`=tan^(-1)""6/17+tan^(-1)""11/23`
`=tan^(-1)((6/17+11/23)/(1-6/17xx11/23))`
`=tan^(-1)(325/325)`
`=tan^(-1) 1`
`=pi/4`
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