Home
Class 11
MATHS
Find a and b such that the following ine...

Find `a and b` such that the following inequality holds good for all `theta` . `alt=3costheta+5sin(theta-pi/6)lt=b`

Text Solution

Verified by Experts

Given,
`=>3cosx+5sin(x−π/6​)`
`=>3cosx+5sinxcos(π/6)​−5cosxsin(​π/6)`
`=>3cosx+(5sqrt(3) ​sinx)/2​−(5/2)cosx`​
`=>(cosx)/2​+(5sqrt(3) ​sinx)/2​`
Using the formula to find maximum and minimum value,
...
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    RD SHARMA|Exercise Solved Examples And Exercises|167 Videos

  • TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES

    RD SHARMA|Exercise Solved Examples And Exercises|193 Videos

Similar Questions

Explore conceptually related problems

Find "a" and "b" such that a lt 3 "cos" theta+5 "sin"(theta-(pi)/(6)) lt b , holds good for all values of theta .

Find the maximum and minimum values of the expression: 3cos theta+5sin(theta-(pi)/(6))

Evaluate the following integrals: int_(0)^( pi/6)cos^(-3)2 theta sin2 theta d theta

Find the maximum and minimum values of the following expressions.(i) 3cos theta+5sin(theta-(pi)/(6))( ii) 4sin theta-3cos theta+7

Find the range of function f(theta)=5sin theta+3sin(theta+(pi)/(3))+2

The value of a+b such that the inequality ale 5 cos theta+3cos (theta+(pi)/(3))+3le b holds true for all the real values of theta is (equality holds on both sides atleast once for real values of theta )

Evaluate the following: |costheta, -sin theta],[sin theta, cos theta]|

Find general solutions of the following equation: (a) costheta= -sqrt(3)/2 (b) tan theta=-1/sqrt(3) (c ) sintheta=tantheta (d) sin 9theta=sin theta

Fill in the blanks ine ach of the following so that that resulting sentence becomes true. If sin theta=2/3, (5pi)/2 lt theta lt 3pi then sin (theta/2) = __________.

RD SHARMA-TRIGONOMETRIC RATIOS OF COMPOUND ANGLES-Solved Examples And Exercises
  1. If tanalpha=1/(1+2^(-x)) and tanbeta=1/(1+2^(x+1)), then write the va...

    Text Solution

    |

  2. If alphaa n dbeta are acute angles such that t a nalpha=m/(m+1)a n dt ...

    Text Solution

    |

  3. Find a and b such that the following inequality holds good for all the...

    Text Solution

    |

  4. Prove that (2sqrt3 + 3) sintheta +2sqrt3 cos theta lies between -(2s...

    Text Solution

    |

  5. Prove that: ("sin"(x+theta))/("sin"(x+phi))=cos(theta-phi)+cot(x+phi)s...

    Text Solution

    |

  6. It cos(alpha+beta)=4/5,sin(alpha-beta)=5/(13)a n dalpha,beta lie betwe...

    Text Solution

    |

  7. If tanA-tanB=x a n dcotB-cotA=y , prove that cot(A-B)=1/x+1/y

    Text Solution

    |

  8. If cos(alpha-beta)+cos(beta-gamma)+cos(gamma-alpha)=-3/2 , prove that...

    Text Solution

    |

  9. If sinB=3sin(2A+B), prove that 2tanA+tan(A+B)=0.

    Text Solution

    |

  10. If 2tanbeta+cotbeta=tanalpha , prove that cotbeta=2tan(alpha-beta)dot

    Text Solution

    |

  11. If the system of linear equations x=cy+bx, y=ax+cz,z=bx+ay has a non t...

    Text Solution

    |

  12. Prove that: tan3Atan2AtanA=t a n3A-tan2A-t a n A cot Acot2A-cot2Aco...

    Text Solution

    |

  13. Prove that: sin^2(pi/8+A/2)-sin^2(pi/8-A/2)=1/sqrt(2)sinA

    Text Solution

    |

  14. Prove that: sin^2A=cos^2(A-B)+cos^2B-2cos(A-B)cosAcosBdot

    Text Solution

    |

  15. If 3t a n At a n B=1, prove that 2cos(A+B)=cos(A-B)dot

    Text Solution

    |

  16. FInd : tan75^0+cot75^0=

    Text Solution

    |

  17. If alphaa n dbeta are the solutions of acostheta+bsintheta=c , then ...

    Text Solution

    |

  18. If alphaa n dbeta are the solutions of the equation at a ntheta+bs e c...

    Text Solution

    |

  19. If (sin(x+y))/(sin(x-y))=(a+b)/(a-b) , show that (tanx)/(tany)=a/b .

    Text Solution

    |

  20. If t a n(pi//4+theta)+t a n(pi//4-theta)=a , then t a n^2(pi//4+theta...

    Text Solution

    |