Evaluate each of the following:

Now first of the principal value of


cosec–1


Let cosec–1 = y


cosec y =


= cosec


The range of principal value of cosec–1 is –{0}


and cosec


Therefore, the principal value of cosec–1 is …(1)


Now, the value of cot–1(–1)


Let cot–1(–1) = y


cot y = –1


= – cot = 1


= cot


= cot


The range of principal value of cot–1is (0, π)


and cot = –1


Therefore, the principal value of cot–1(–1) is …(2)


From (1) and (2) we can write the given equation as


=


=


=


3