Find the value of `tan^(-1)(-1/(sqrt(3)))+cot^(-1)((1)/(sqrt(3))) + tan^(-1)[sin'((-pi)/(2))]`.

Answer

N/a

Explanation

We have, `tan^(-1)(-(1)/(sqrt(3)))+cot^(-1)'((1)/(sqrt(3)))+tan^(-1)[sin((-pi)/(2))]`
`= tan^(-1)(tan'(5pi)/(6))+cot^(-1)(cot'(pi)/(3))+tan^(-1)(-1)`
`= tan^(-1)[tan(pi - (pi)/(6))]+cot^(-1)[cot(pi/3)]+tan^(-1)[tan(pi-(pi)/(4))]`
`=tan^(-1)(-tan'(pi)/(6))+cot^(-1)(cot'(pi)/(3))+tan^(-1)(-tan'(pi)/(4))`
`[{:( :'" "tan^(-1)(tanx)=x,x in(-pi/2,pi/2)),(" "cot^(-1)(cotx)=x,x in(0,pi)),(and tan^(-1)(-x)=,-tan^(-1)x):}]`
`= - (pi)/6 + (pi)/(3) - (pi)/(4) = (-2pi xx 4 pi - 3pi)/(12)`
` = (-5pi+4pi)/(12) = -(pi)/(12)`