RD Sharma - Mathematics (Volume 1)

Book: RD Sharma - Mathematics (Volume 1)

Chapter: 4. Inverse Trigonometric Functions

Subject: Maths - Class 12th

Q. No. 1 of Exercise 4.5

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

1

Find the principal values of each of the following:

cosec–1(2cos)


Let us assume 2cos = θ


We know cos =


2cos = 2


2cos = –1


The question converts to cosec–1(–1)


Now,


cosec–1–1 = y


cosec y = –1


–cosec y = 1


–cosec = 1


As we know cosec(–θ) = –cosecθ


–cosec = cosec


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


cosec = –1


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


Chapter Exercises

More Exercise Questions