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The value of `tan^(-1)1/3+tan^(-1)1/5+tan^(-1)1/7+tan^(-1)1/8` is ……..A. `(11pi)/5`B. `pi/4`C. `pi`D. `(3pi)/4` |
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Answer» Correct Answer - B We have , `tan^(-1).(1)/(3) + tan^(-1).(1)/(5) + tan^(-1) tan^(-1).(1)/(7) + tan ^(-1).(1)/(8)` `rArr tan^(-1)(((1)/(3)+(1)/(5))/(1-(1)/(3) xx (1)/(5))) + tan^(-1).(((1)/(7)+(1)/(8))/(1-(1)/(7) xx (1)/(8)))` `(because tan ^(-1) x + tan^(-1) y = tan^(-1)((x+y)/(1-xy)))` `= tan^(-1) ((8)/(14)) + tan^(-1)((15)/(55)) = tan^(-1)((4)/(7)) + tan^(-1)((3)/(11))` `= tan^(-1).(((4)/(7) +(3)/(11))/(1-(4)/(7) xx (3)/(11))) = tan^(-1)((44+21)/(77-21))` `=tan^(-1)((65)/(65)) = tan^(-1) (1) = (pi)/(4)` |
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