Q. 3 A4.0( 2 Votes )

# Evaluate each of

Answer :

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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