find the exact value of the expression tan1tanpi8SolutionLet

find the exact value of the expression: tan^-1[tan(-pi/8)]

Solution

Let tan^-1[ tan ( - pi/ 8)] = @

tan @ = tan( - pi/8)

tan @ = - tan ( pi/8) [ tan ( - theta) = - tan( theta)]

tan @ = tan ( pi - pi/8)

tan @ = tan ( 7 pi/8)

@ = 7 pi/8

Ans = tan^-1[tan(-pi/8)] = 7*pi / 8