Question

Write the value of `sin^-1((-sqrt3)/2)+cos^-1((-1)/2)`

Answer 1

`sin^-1(-x)=-sin^-1x,x in[-1,1]`

`cos^-1(-x)=pi-cos^-1x,x in[-1,1]`

`therefore sin^-1(-(sqrt3)/2)+cos^-1(-1/2)`

`=-sin^-1(sqrt3/2)+pi-cos^-1(1/2)`

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

`=-pi/3+pi-pi/3`

`=pi/3`

`thereforesin^-1(-sqrt3/2)+cos^-1(-1/2)=pi/3`