Home
Class 11
MATHS
If the set of all values of x in (-pi...

If the set of all values of `x` in `(-pi/2,pi/2)` satisfying `|4sinx+sqrt(2\ )+|

Text Solution

Verified by Experts

`|4sinx+sqrt(2)| lt sqrt(6)`
`rArr -sqrt(6) lt 4sinx + sqrt(2) lt sqrt(6) rArr -sqrt(6) - sqrt(2) lt 4sinx lt sqrt(6) -sqrt(2)`
`rArr (-sqrt(6)+sqrt(2))/4 lt sinx lt (sqrt(6)-sqrt(2))/4 rArr -sqrt(6)- sqrt(2) lt 4sin x lt sqrt(6) - sqrt(2)`
`rArr -(sqrt(6) + sqrt(2))/4 lt sinx lt (sqrt(6)-sqrt(2))/(4) rArr -(5pi)/(12) lt x lt pi/12` for `x in (-pi/2, pi/2)`
Comparing with `(api)/(24) lt x lt (bpi)/24`, we get `a=-10, b=2`
`|(a-b)/3|=|(-10-2)/(3)|=4`
Promotional Banner

Topper's Solved these Questions

  • BASIC MATHS,LOGARITHIM, TRIGNOMETRIC RATIO AND IDENTITIES AND TRIGNOMETRIC EQUATION

    ALLEN|Exercise DO YOURSELF|20 Videos

  • BASIC MATHS,LOGARITHIM, TRIGNOMETRIC RATIO AND IDENTITIES AND TRIGNOMETRIC EQUATION

    ALLEN|Exercise DO YOURSELF 1|2 Videos

  • BASIC MATHS LOGARITHIM TRIGNOMETRIC RATIO AND IDENTITIES AND TRIGNOMETRIC EQUATION

    ALLEN|Exercise ILLUSTRATIONS|39 Videos

  • SOLUTION AND PROPERTIES OF TRIANGLE

    ALLEN|Exercise All Questions|62 Videos

Similar Questions

Explore conceptually related problems

the set of all x in (-(pi)/(2),(pi)/(2)) satisfying |4sin x-1|=sqrt(5) is givenby

The set of all x in ((-pi)/(2),(pi)/(2)) satisfying |4sin x-1|

The set of all x in (-pi,pi) satisfying |4 sin x-1| lt sqrt(5) is given by

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

Find the set of all x in (-(pi)/(2),(pi)/(2)) which satisfy | 4 sin x-1| lt sqrt(5)

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

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

The sum of all values of theta in (0 , pi) satisfying sin^(2) 2 theta + cos^(4) 2 theta = 1 is:

Set of all real values of x satisfying the inequation sqrt(4-x^(2))>=(1)/(x) is

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

ALLEN-BASIC MATHS,LOGARITHIM, TRIGNOMETRIC RATIO AND IDENTITIES AND TRIGNOMETRIC EQUATION -EXERCISE (S-1)
  1. If the set of all values of x in (-pi/2,pi/2) satisfying |4sinx+sqr...

    Text Solution

    |

  2. Solve the following equations where x in R a) (x-1)|x^(2)-4x+3|+2x^(...

    Text Solution

    |

  3. Consider the function f(x) =|x-1|-2|x+2|+|x+3|

    Text Solution

    |

  4. Find the square of the sum of the roots of the equation log(3)x.log(...

    Text Solution

    |

  5. Find the value of 49^(1-log(7)2)+5^(-log(5)4)

    Text Solution

    |

  6. if a,b,c are positive real numbers such that a^(log3(7));b^(log7(11))=...

    Text Solution

    |

  7. Solve for x: a) (log(10)(x-3))/(log(10)(x^(2)-21)) = 1/2 b) log(lo...

    Text Solution

    |

  8. If x,y>0 logy x+logx y=10/3 and xy=144 then (x+y)/2=sqrtN where N is a...

    Text Solution

    |

  9. Solve the system of equations: (log)a x(log)a(x y z)=48(log)a y loga(x...

    Text Solution

    |

  10. Solve the equation for x:x^(logx+4) = 32, where base of logarithim is ...

    Text Solution

    |

  11. Find the product of the positive roots of the equation sqrt((2008))...

    Text Solution

    |

  12. Solve the inequality: log(1//2)(x+1) gt log(2)(2-x)

    Text Solution

    |

  13. Solve the inequality: log(x)2.log(2x)2. log(2)4x gt 1

    Text Solution

    |

  14. Prove that : cos^2alpha+cos^2(alpha+beta)-2cosalphacosbetacos(alpha+be...

    Text Solution

    |

  15. Prove that 2 sin^2 beta + 4 cos(alpha + beta) sin alpha sin beta + co...

    Text Solution

    |

  16. sin^4(pi/16)+sin^4(3pi/16)+sin^4(5pi/16)+sin^4(7pi/16)=3/2

    Text Solution

    |

  17. If x=sin(theta+(7pi)/(12))+sin(theta+pi/(12))+sin(theta+(3pi)/(12))dot...

    Text Solution

    |

  18. 6. Find the positive integers p, q, r, s satisfying tan (pi/24)=(sqrt(...

    Text Solution

    |

  19. if m*tan(theta-30)=n*tan(theta+120), show that cos2theta=(m+n)/(2(m-n)...

    Text Solution

    |

  20. If cos(alpha+beta)=4/5; sin(alpha-beta)=5/13 and alpha,beta lie betwee...

    Text Solution

    |

  21. If the value of the expression sin 25^@* sin 35^@* sin 85^@ can be exp...

    Text Solution

    |