Home
Class 12
MATHS
Let A=sin^6theta+cos^8theta, " then "A("...

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

A

1

B

`1/2`

C

`3/2`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
We know that `0 le sin^2thetale1`
`rArr sin^8thetagesin^2theta`
Similarly, `cos^14thetalecos^2theta`
On adding, we get
`sin^8theta+cos^14thetalesin^2theta+cos^2theta`
`orsin^8theta+cos^14thetalt1`
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

If sin theta = cos theta then 2 theta =

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

If A=sin^(8) theta + cos^(14) theta , then for all values of theta ,

If sin2 theta = cos 3 theta then theta =

sin4theta cos 2theta = cos5theta sin theta

If A(theta)=[(sin theta, i cos theta),(i cos theta, sin theta)] , then which of the following is not true ?

If the co-ordinates of a variable point P be (cos theta + sin theta, sin theta - cos theta) where theta is the perimeter, then the locus of P is :

Express (cos theta - sin theta)" in the form " r cos (theta+ alpha) and (sqrt 3sin theta + cos theta) " in the form r" sin(theta + beta).

If sin 6 theta =32 cos ^(5) theta sin theta -32 cos ^(3) theta sin theta + 3x, then the value of x is-

CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS -Exercises
  1. If thetaigt0" for "1lethetalenandtheta1+theta2+theta3+...+thetan=pithe...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  13. The minimum value of the function f(x)=sinx/(sqrt(1-cos^2x))+cosx/sqrt...

    Text Solution

    |

  14. If abs(cos theta{sin theta+sqrt(sin^2theta+sin^2alpha)})lek, then the ...

    Text Solution

    |

  15. In which of the following intervals the inequality, sinx < cos x < tan...

    Text Solution

    |

  16. Th range of k for which the inequaliity kcos^2x-kcosx+1>=0 AA x in(-o...

    Text Solution

    |

  17. The value of cos(pi/7)+cos((2pi)/7)+cos((3pi)/7)+cos((4pi)/7)+cos((5pi...

    Text Solution

    |

  18. The numerical value of tan(pi/3)+2tan((2pi)/3)+4tan((4pi)/3)is equal t...

    Text Solution

    |

  19. The expression 3{sin^4((3pi/2)-alpha)+sin^4(3pi-alpha)} -2{sin^6(pi/2+...

    Text Solution

    |

  20. The value of the expression log10(tan6^@)+log10(tan12^@)+log10(tan18^@...

    Text Solution

    |