Q. 3 A4.0( 2 Votes )

# Evaluate each of

Let cot–1() = y

cot y =

= – cot

= cot

= cot

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

and cot

The principal value of cot–1() is …(1)

Let,

cosec–1–2 = z

cosec z = –2

–cosec z = 2

–cosec = 2

As we know cosec(–θ) = –cosecθ

–cosec = cosec

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

cosec = –2

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

Let sec–1 = w

sec w =

= sec

The range of principal value of sec–1is [0, π]–{}

and sec

Therefore, the principal value of sec–1() is …(3)

From (1), (2) and (3) we can write the above equation as

=

=

=

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