Home
Class 12
MATHS
The least value of 3sin^2theta+4cos^2the...

The least value of `3sin^2theta+4cos^2theta` is

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
B
`sin^4theta+cos^4theta=2(sin^2theta+cos^2theta)+cos^2theta`
`=2+cos^2thetagt2 [:'cos^2thetagt0]`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|17 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Linked Comprehension Type|11 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Concept Application Exercises 2.14|1 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE PUBLICATION|Exercise Archives (Numerical value type)|4 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|2 Videos

Similar Questions

Explore conceptually related problems

The least value of 2sin^2theta+3cos^2theta is

Find the least value of (2 sin^(2)theta+3 cos^(2)theta) .

3sin^(2)theta + 7cos^(2)theta=6

Find the maximum value of 1/2sin^2theta+1/3cos^2theta

If cos theta -4 sin theta =1, then the value of (sin theta+4 cos theta) is-

The value of (sin ^(6)theta + cos ^(6) theta + 3sin^(2) theta cos ^(2)theta) is-

If 3 sin theta + 5 cos theta = 5 , then the value of 5 sin theta - 3 cos theta will be-

If 2 sin theta cos theta = 1 , then find the value of sin theta-cos theta .

"If " pi/2 < theta lt pi and 5 sin ^(2) theta + 3 cos^(2) theta = 4, find the values of sin 2 theta and cos 3 theta.

If x=(2 sin theta)/(1+ sin theta + cos theta) then the value of (1+ sin theta - cos theta)/(1+ sin theta)

CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS -Exercises
  1. If π<α<(3π)/2 then sqrt((1-cosalpha)/(1+cosalpha))+sqrt((1+cosalpha)/...

    Text Solution

    |

  2. If 0 < alpha < pi/ 6 then alpha(cosec alpha) is

    Text Solution

    |

  3. The least value of 3sin^2theta+4cos^2theta is

    Text Solution

    |

  4. The minimum value of sin^4theta+cos^4theta is

    Text Solution

    |

  5. If f(x)=sin^6x+cos^6x , then range of f(x) is [1/4,1] (b) [1/4,3/4] ...

    Text Solution

    |

  6. The minimum value of atan^2x+bcot^2x equals the maximum value of asin^...

    Text Solution

    |

  7. Range of f(theta)=cos^2theta(cos^2theta+1)+3sin^2theta is

    Text Solution

    |

  8. If 0<theta<pi, then minimum value of 3sintheta+cos e c^3theta is 4 (b)...

    Text Solution

    |

  9. If thetaigt0" for "1lethetalenandtheta1+theta2+theta3+...+thetan=pithe...

    Text Solution

    |

  10. The set of values of lambda in R such that sin^2theta+costheta=lambda...

    Text Solution

    |

  11. Let A=sin^6theta+cos^8theta, " then "A("max") is

    Text Solution

    |

  12. Minimum value of y=25sin^2x+36cos e c^2xAAx in R is

    Text Solution

    |

  13. If aa n db are positive quantities such that a > b , the minimum value...

    Text Solution

    |

  14. If y=(cosx+secx)^2+(tanx+cotx)^2 then the minimum value of y,AAx in R,...

    Text Solution

    |

  15. The variable x satisfying the equation |sinxcosx|+sqrt(2+tan^2+cot^2x)...

    Text Solution

    |

  16. If the equation cot^4x-2cos e c^2x+a^2=0 has at least one solution, th...

    Text Solution

    |

  17. If cos^2x-(c-1)cosx+2cgeq6 for every x in R , then the true set of va...

    Text Solution

    |

  18. If the inequality sin^2x+acosx+a^2>1+cosx holds for any x in R , then...

    Text Solution

    |

  19. If 0 lt alpha lt pi/2, then sqrt(2cotalpha+1/(sin^2alpha)) is equal t...

    Text Solution

    |

  20. The value of sectheta/sqrt(1+tan^2theta)+(cosectheta)/(sqrt(1+cot^2th...

    Text Solution

    |