The value of the expression `sin^(-1)(sin(22pi)/7)+cos^(-1)(cos(5pi)/3)+tan^(-1)(tan(5pi)/7)+` `sin^(-1)(cos2)` is (a) `(17pi)/(42)-2` (b) `-2` (c)`(-pi)/(21)-2` (d) `non eoft h e s e`

Options

A. `(17 pi)/(42) -2`
B. `-2`
C. `(-pi)/(21) -2`
D. none of these

Answer

A

Explanation

`sin^(-1) sin((22pi)/(7)) = sin^(-1) sin(3pi + (pi)/(7)) = - (pi)/(7)`
`cos^(-1) cos ((5pi)/(3)) = cos^(-1) cos (2pi - (pi)/(3)) = (pi)/(3)`
`tan^(-1) tan ((5pi)/(7)) = tan^(-1) tan(pi - (2pi)/(7)) = - (2pi)/(7)`
`sin^(-1) cos (2) = (pi)/(2) - cos^(-1) cos 2 = (pi)/(2) -2`
`:.` Required value `= - (pi)/(7) + (pi)/(3) - (2pi)/(7) + (pi)/(2) - 2`
`= ((-18 + 35) pi)/(42) -2`
`= (17 pi)/(42) - 2`