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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
=
=
=