RD Sharma - Mathematics (Volume 1)

Book: RD Sharma - Mathematics (Volume 1)

Chapter: 4. Inverse Trigonometric Functions

Subject: Maths - Class 12th

Q. No. 3 of Exercise 4.6

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3

Evaluate each of the following:

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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