InterviewSolution
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InterviewSolution
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Find the value of `2 cos^(-1).(3)/(sqrt13) + cot^(-1).(16)/(63) + (1)/(2) cos^(-1).(7)/(25)` |
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Answer» `E = 2 cos^(-1).(3)/(sqrt13) + cot^(-1).(16)/(63) + (1)/(2) cos^(-1).(7)/(25)` `= 2 tan^(-1).(2)/(3) + tan^(-1).(63)/(16) + (1)/(2) cos^(-1).(7)/(25)` Now, `2 tan^(-1).(2)/(3) = tan^(-1). (2 ((2)/(3)))/(1 - (4)/(9))` `= tan^(-1).(12)/(5)` Let `(1)/(2) cos^(-1).(7)/(25) = tan^(-1) x` `rArr cos^(-1).(7)/(25) = 2 tan^(-1) x` `rArr tan^(-1).(24)/(7) = tan^(-1).(2x)/(1 - x^(2))` `rArr (24)/(7) = (2x)/(1 - x^(2))` `rArr 12x^(2) + 7x - 12 = 0` `rArr (4x -3) (3x + 4) = 0` `rArr x = 3//4` `:. E = tan^(-1).(12)/(5) + tan^(-1).(63)/(16) + tan^(-1).(3)/(4)` `= pi + tan^(-1).((12)/(5) + (3)/(4))/(1-((12)/(5)) ((3)/(4))) + tan^(-1).(63)/(16)` `= pi + tan^(-1) (-(63)/(16)) + tan^(-1).(63)/(16)` `= pi` |
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