Find the value of `tan^(-1)(1) + cos^(-1) (-1/2) + sin^(-1) (-1/2)`

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#### Solution

Let `tan^(-1) (1)` = x Then tan x= 1 = tan `pi/4`

`:. tan^(-1) (1) = pi/4`

Let `cos^(-1) (-1/2) = y` Then, `cos y = -1/2 = -cos(pi/3) = cos(pi - pi/3) = cos ((2pi)/3)`

`:. cos^(-1) (- 1/2) = (2pi)/3`

Let `sin^(-1) (-1/2) = z`. Then `sin z =-1/2 = -sin(pi/6) = sin(-pi/6)`

`:. sin^(-1)(-1/2) = - pi/6`

`:. tan^(-1) (1) + cos^(-1) (-1/2) + sin^(-1) (-1/2)`

`= pi/4 + (2pi)/3 - pi/6`

`= (3pi + 8pi - 2pi)/12 = (9pi)/12 = (3pi)/4`

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