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Question
Find the value of `tan^-1 (sqrt(3)) - sec^-1 (- 2)`
Solution
x = `tan^-1 (sqrt(3))`
tan x = `sqrt(3) = tan pi/3`
x = `pi/3`
y = `sec^-1(- 2)`
sec y = ` - 2 = - sec pi/3`
sec y = `sec(pi - pi/3)`
sec y = `sec(2 pi/3)`
y = `(2 pi/3)`
`tan^-1 (sqrt(3)) - sec^-1(- 2) = pi/3 - (2pi)/3`
= `(pi - 2pi)/3`
= `- pi/3`
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