The complete set of values of x satisfyi...

The complete set of values of x satisfying the inequality `sin^(-1)(sin 5) gt x^(2)-4x` is `(2-sqrt(lambda-2pi), 2+sqrt(lambda-2pi))`, then `lambda=`

A

`x in (2+sqrt(9-2pi) , oo)`

B

`x in 2-sqrt(9-2pi),2+sqrt(9-2pi)`

C

`x in 2-sqrt(9-2pi),oo`

D

none of these

Text Solution

Verified by Experts

We have
`sin^(-1)(sin5)gtx^(2)-4x`
`rarr sin^(-1)sin(5-2pi)gtx^(2)-4x`
`rarr 5-2 pi gt x^(2)-4x`
`rarr x^(2)-4x-5+2pilt0 rarr -sqrt(9-2pi)ltxlt2+sqrt(9-2pi)`

Promotional Banner

Promotional Banner

Topper's Solved these Questions

INVERSE TRIGONOMETRIC FUNCTIONS
OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|11 Videos
INVERSE TRIGONOMETRIC FUNCTIONS
OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|72 Videos
INVERSE TRIGONOMETRIC FUNCTIONS
OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos
INDEFINITE INTEGRALS
OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos
LIMITS
OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|58 Videos

Similar Questions

Explore conceptually related problems

The complete set of values of x, x in (-(pi)/(2), pi) satisfying the inequality cos 2x gt |sin x| is :

The set of values of x in (-pi, pi) satisfying the inequation |4"sin" x-1| lt sqrt(5) , is

The set of all real numbers satisfying the inequation 2^(x)+2^(|x|) gt 2sqrt(2) , is

Set of values of x lying in [0, 2pi] satisfying the inequality |sin x | gt 2 sin^(2) x contains

The set of all real values of x satisfying sin^(-1)sqrt(x)lt(pi)/(4) , is

If the maximum value of x which satisfies the inequality sin^(-1)(sinx) ge cos^(-1)(sinx)" for "x in (pi)/(2), 2pi" is " lambda, then (2lambda)/(3) is equal to (take pi=3.14 )

The vaue of x satisfying sin^(-1)(x)+sin^(-1)(sqrt(15)x)=(pi)/2 is

The number of values of x in [0, 4 pi] satisfying the inequation |sqrt(3)"cos" x - "sin"x|ge2 , is

The number of values of x in [0,2pi] satisfying the equation |cos x – sin x| >= sqrt2 is

The complete set of values of x satisfying ( 2 sin 6x)/(sin x -1) lt 0 and sec^(2) x - 2sqrt(2) tan x le 0 in (0, (pi)/(2)) is [ a,b) cup (c, d], then find the value of ((cd)/(ab)) .

OBJECTIVE RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTIONS -Section I - Solved Mcqs

The solution set of the equation cos^(-1)x-sin^(-1)x=sin^(-1)(1-x) i...
Text Solution
|
Number of triplets (x, y, z) satisfying sin^(-1)x+cos^(-1)y+sin^(-1)z=...
Text Solution
|
The complete set of values of x satisfying the inequality sin^(-1)(si...
Text Solution
|
If cos^(-1)(cos 4)gt3x^(2)-4x then
Text Solution
|
The number of real solutions (x, y), where |y|= sin x , y= cos^(-1)(c...
Text Solution
|
If u=cot^(-1)sqrt(cos theta) -tan^(-1)sqrt(cos theta) then sin u=
Text Solution
|
A value of x satisfying tan(sec^(-1)x)=sin(cos^(-1).(1)/sqrt5) is
Text Solution
|
The number of the solutions of the equation 2 sin^(-1) sqrt(x^(2) + x ...
Text Solution
|
If alpha, beta and gamma are the three angles with alpha = 2tan^(-1)(s...
Text Solution
|
If f(x) = cos^(-1)x + cos^(-1){(x)/(2)+(1)/(2)sqrt(3-3x^(2))} then :
Text Solution
|
The trigonometric equation sin^(-1)x=2sin^(-1)a has a solution for all...
Text Solution
|
If alpha is the only real root of the equation x^(3) + bx^(2) + cx + 1...
Text Solution
|
If tan^(-1)(a/x)+tan^(-1)(b/x)+tan^(-1)(c /x)+tan^(-1)(d/x)=(pi)/(2) t...
Text Solution
|
Let u = cot^(-1) sqrt(cos 2 theta) - tan^(-1) sqrt( cos 2 theta) , ...
Text Solution
|
If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi , prove that: xsqrt(1-x^2)+ysqrt(1...
Text Solution
|
If cos^(-1) sqrtp + cos^(-1) sqrt(1 -p) + cos^(-1) sqrt(1 - q) = (3pi)...
Text Solution
|
The solution set of the equation sin^(-1)x=2 tan^(-1)x is
Text Solution
|
If cot(cos^(-1)x)=sec{tan^(-1)((a)/sqrt(b^(2)-a^(2)))} then x equals
Text Solution
|
tan^(-1)[(C(1)x-y)/(c(1)y+x)]+tan^(-1)[(C(2)-C(1))/(1+C(1)C(2))]..+tan...
Text Solution
|
about to only mathematics
Text Solution
|