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 4.5

Listen NCERT Audio Books to boost your productivity and retention power by 2X.

3

For the principal values, evaluate the following:

Let,


Sin–1 = y


sin y =


–sin y =


–sin


As we know sin(–θ) = –sinθ


–sin = sin


The range of principal value of sin–1 is and sin


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


Let,


cosec–1 = z


cosec z =


–cosec z =


–cosec


As we know cosec(–θ) = –cosecθ


–cosec = cosec


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


cosec


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


From (1) and (2) we get



=


Chapter Exercises

More Exercise Questions