Question

cosec-1 (-\(\sqrt{2}\))

Answer 1

Let cosec-1(-\(\sqrt{2}\)) = y

∴ cosec y = –\(\sqrt{2}\) = – cosec\(\frac { π }{ 4 }\) = cosec (- \(\frac { π }{ 4 }\)).

The range of principal value branch of cosec-1 is (- \(\frac { π }{ 2 }\), \(\frac { π }{ 2 }\)) – {0}

∴ principal value of cosec-1(-\(\sqrt{2}\)) is – \(\frac { π }{ 4 }\).