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`

Explanation

`sin^-1(sin((22pi)/7)) + cos^-1(cos((5pi)/3))+tan^-1(tan((5pi)/7)) + sin^-1(cos2)`

`=sin^-1(sin(3pi+pi/7)) + cos^-1(cos(2pi-pi/3)+tan^-1(tan(pi-(2pi)/7)) + pi/2-cos^-1(cos2)`

`=-sin^-1(sin(pi/7)) + cos^-1(cos(pi/3))-tan^-1(tan((2pi)/7)) + pi/2-2`

`=-pi/7+pi/3-(2pi)/7+pi/2 - 2`

`=(17pi)/42 - 2`

So, option `a` is the correct option.