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Question
Find the value of `cot^-1(1) + sin^-1 (- sqrt(3)/2) - sec^-1 (- sqrt(2))`
Solution
x = `cot^-1(1)`
y = `sin^-1(- sqrt(3)/2)`
cot x = 1 = `cot pi/4`
sin y = `- sqrt(3)/2 = sin (- pi/3)`
x = `pi/4`
y = `- pi/3`
z = `sec^-1 (- sqrt(2))`
sec z = `- sqrt(2)`
sec z = `- sec pi/4`
= `sec(pi - pi/4)`
= `sec (3pi)/4`
z = `+ (3pi)/4`
`cot1(1) + sn-1(- sqrt(3)/2) - sec^-1(- sqrt(2))`
= `pi/4 - pi/3 - (3pi)/4`
= `- pi/3 - (2pi)/4`
= `- pi/3 - pi/2`
= `- (5pi)/6`
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