Find the value of `cot^(-1)(-sqrt3)+cosec^(-1)(2)+sec^(-1)(-sqrt2)`.

Explanation

Since the principal values of `cot^(-1)x,cosec^(-1)x and sec^(-1)x"lie in "(0,pi), {-pi/2,pi/2]-{0} and [0.pi]-{pi/2}` respectively and in these intervals `cot ((5pi)/6)=-sqrt3,cosec.(pi/6)=2,sec((3pi)/4)=-sqrt2`
`:.cot^(-1)(-sqrt3)=(5pi)/6,cosec^(-1)(2)=pi/6,sec^(-1)(-sqrt2)=(3pi)/4`
`:. cot^(-1)(-sqrt3)+cosec^(-1)(2)=pi/6,sec^(-1)(-sqrt2)=(3pi)/4`
`:.cot^(-1)(-sqqrt3)+cosec^(-1)(2)+sec^(-1)(-sqrt2)`
`(5pi)/6+pi/6+(3pi)/4`
`=(7pi)/4`