Home
Class 11
MATHS
Let A=sin^8theta+cos^(14)theta; then for...

Let `A=sin^8theta+cos^(14)theta;` then for all real `theta`

Text Solution

Verified by Experts

We know, `0 le sin^2theta le 1`
`:. (sin^2theta)^4 le sin^2 theta`
`=>sin^8theta le sin^2 theta->(1)`
Similarly,
`0 le cos^2theta le 1`
`:. (cos^2theta)^7 le cos^2 theta`
`=>cos^14theta le cos^2 theta->(2)`
Now, adding (1) and (2),
...
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE|Exercise Solved Examples And Exercises|381 Videos

Similar Questions

Explore conceptually related problems

If A = sin^2 theta+ cos^4 theta , then for all real values of theta

Let A=sin^8theta+cos^14theta, " then "A_("max") is

The expression cos 3 theta + sin 3 theta + (2 sin 2 theta-3) (sin theta- cos theta) is positive for all theta in

The maximum value of 1+sin(pi/4+theta)+2cos(pi/4-theta) for real values of theta is

If sintheta(1+sin^(2)theta)=cos^(2)theta , then prove that cos^(6)theta-4cos^(2)theta+8cos^(2)theta=4

Prove that sin^(4) theta + cos^(4) theta = 1 - 2 sin^2 theta cos^(2) theta

If sin theta + cos theta theta = sqrt(2) cos theta then cos theta - sin theta is

If cos theta+sin theta=sqrt(2)cos theta then prove that cos theta-sin theta=sqrt(2)sin theta

If sin^(3) theta+sin theta cos theta+ cos^(3) theta=1 , then theta is equal to (n in Z)

Prove that sin (30^(@) + theta) + cos (60^(@) + theta) = cos theta

CENGAGE-TRIGONOMETRIC FUNCTIONS-Solved Examples And Exercises
  1. If sin(A-B)=1/(sqrt(10 ,))cos(A+B)=2/(sqrt(29)), find the value of tan...

    Text Solution

    |

  2. There exists a value of theta between 0 and 2pi that satisfies the equ...

    Text Solution

    |

  3. Let A=sin^8theta+cos^(14)theta; then for all real theta

    Text Solution

    |

  4. If 3tanthetatanphi=1 , then prove that 2cos(theta+phi) = cos(theta-phi...

    Text Solution

    |

  5. Minimum value of y=256sin^2x+324cos e c^2x,AAx in R is (a) 432 (b) 5...

    Text Solution

    |

  6. If (cos^2x+1/(cos^2x)) (1+tan^2 2y)(3+sin3z)=4, then x is an integral ...

    Text Solution

    |

  7. A circle is inscribed in a triangle A B C touching the side A B at D s...

    Text Solution

    |

  8. In a triangle ABC, if sinAsin(B-C)=sinCsin(A-B), then prove that cotA...

    Text Solution

    |

  9. The minimum value of the expression sin alpha + sin beta+ sin gamma, ...

    Text Solution

    |

  10. In A B C ,cotA/2+cotB/2+cotC/2 is equal to Delta/(r^2) (b) ((a+b+...

    Text Solution

    |

  11. The value of theta in (0,2pi) for which 2sin^2theta-5sintheta+2>0 is (...

    Text Solution

    |

  12. In A B C , if cotA+cotB+cotC=0 then find the value of cosAcos BcosC

    Text Solution

    |

  13. Show that tan1^0tan2^0.....tan89^0=1

    Text Solution

    |

  14. In triangle ABC, the line joining the circumcenter and incenter is ...

    Text Solution

    |

  15. The number of solutions of the pair of equations 2sin^2 theta - cos(2 ...

    Text Solution

    |

  16. Given A=sin^2theta+cos^4theta, then for all real theta, (a)1lt=Alt...

    Text Solution

    |

  17. If A ,B ,C ,D are angles of a cyclic quadrilateral, then prove that c...

    Text Solution

    |

  18. The number of distinct real roots of |sinxcosxcosxcosxsinxcosxcosxcosx...

    Text Solution

    |

  19. if ( cos A + cos B )/( sin A + sin B ) = k ( (sin A - sin B)/ ( ...

    Text Solution

    |

  20. cos(alpha-beta)=1a n dcos(alpha+beta)=l/e , where alpha,betamu in [-pi...

    Text Solution

    |