Home
Class 12
MATHS
Find the possible values of sin^(-1) (1 ...

Find the possible values of `sin^(-1) (1 - x) + cos^(-1) sqrt(x -2)`

A

0

B

`{-1,1}

C

2

D

-1/2

Text Solution

Verified by Experts

The correct Answer is:
A
We have `f(x) = sin^(-1) (1 - x) + cos^(-1) sqrt(x - 2)`
We must have `- 1 le (1 - x) le 1`
`rArr -2 le - x le 0`
`rArr 0 le x le 2 and x -2 ge 0`
`rArr 0 le x le 2 and x le 2`
`:. X = 2`
Thus, expression is defined only for `x = 2`
`:. f(2) = sin^(-1) (-1) + cos^(-1) (0)`
`= (-pi//2) + (pi//2)`
`=0`
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise 7.2|6 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise 7.3|12 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Question Bank|24 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise JEE Previous Year|20 Videos

  • JEE 2019

    CENGAGE|Exercise Chapter 10|9 Videos

Similar Questions

Explore conceptually related problems

Find the value of : sin (sin^(-1) x + cos^(-1) x)

Find the value of x if sin^(-1)(1/8)=cos^(-1)x

Find all possible values of x and y for which cos^(-1)sqrtx+cos^(-1)sqrt(1-x)+cos^(-1)sqrt(1-y)=((3pi)/4)

Prove that sin^(-1)x=cos^(-1) sqrt(1-x^2)

Find the value of sin^(-1)x+sin^(-1)sqrt(1-x^(2))

sin^(-1)x=cos^(-1)sqrt(1-x^(2))

cos^(-1)sqrt(1-x)+sin^(-1)sqrt(1-x)=

Find the value of sin^(-1)(cos(sin^(-1)x))+cos^(-1)(sin(cos^(-1)x))

Find the value of cos^(-1)(x)+cos^(-1)((x)/(2)+(sqrt(3-3x^(2)))/(2))

Find the value of : tan^(-1) ((-1)/(sqrt(3)))+cos^(-1)((-sqrt(3))/2)+sin^(-1)(1/2)