Question

tan^-1(tan\(\frac { 3π }{ 4 }\))

Answer 1

tan^-1(tan \(\frac { 3π }{ 4 }\) ) = tan^-1 tan(π – \(\frac { π }{ 4 }\))
= tan^-1(- tan\(\frac { π }{ 4 }\))
= tan^-1[tan(\(\frac { -π }{ 4 }\)) ] = – \(\frac { π }{ 4 }\)
Again note that tan^-1 tan\(\frac { 3π }{ 4 }\) ≠ \(\frac { 3π }{ 4 }\),
since the range of principal values branch of tan^-1 is ( \(\frac { -π }{ 2 }\), \(\frac { π }{ 2 }\) )