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