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  • Need solution for RD Sharma Maths Class 12 Chapter 3 Inverse Trigonometric Functions Excercise Fill in the Blanks Question 35

Need solution for RD Sharma Maths Class 12 Chapter 3 Inverse Trigonometric Functions Excercise Fill in the Blanks Question 35

Answers (1)

Answer:

              (-\infty,-1]\cup [1,\infty)

Hints:

You must have known about the principal values and range of inverse trigonometric function

Given:

                y=\sec^{-1}x

Solution:

 y=\sec^{-1}x

The range of principal value branch of y=\sec^{-1}x

Principal value branch of y=\sec^{-1}x is\left [ 0,\pi \right ]-\left \{ \frac{\pi}{2} \right \}

And the range is in \left ( 1,\infty \right ) it is increasing and \left (-\infty,-1 \right ) it is increasing

The function does not have any inflection points

\thereforeThe range of y=\sec^{-1}x is (-\infty,-1]\cup [1,\infty)

 

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