Home
Class 11
MATHS
Prove that: cos ^(4) ""(pi)/(8) + cos ^(...

Prove that:` cos ^(4) ""(pi)/(8) + cos ^(4) ""(3pi)/(8) + sin ^(4) "" (5pi)/(8) + sin ^(4)""(7pi)/(8) = 3/2.`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMPOUND AND MULTIPLE ANGLES

    ICSE|Exercise CHEPTER TEST |23 Videos

  • COMPOUND AND MULTIPLE ANGLES

    ICSE|Exercise EXERCISE 5 (C ) |30 Videos

  • COMPLEX NUMBERS

    ICSE|Exercise Chapter Test|25 Videos

  • CONIC SECTIONS

    ICSE|Exercise Multiple Choice Questions |33 Videos

Similar Questions

Explore conceptually related problems

Prove that cos ^(4) ""(pi)/(8) + cos ^(4) ""(3pi)/(8) + cos ^(4) ""(5pi)/(8) + cos ^(4) "" (7pi)/(8) = (3)/(2)

sin ^(4) "" (pi)/(8) + sin ^(4) "" (3pi)/(8) + sin ^(4) "" (5pi)/(8) + sin ^(4)"" (7pi)/(8) = (3)/(2).

Prove that: cos^(2)((pi)/(8)) + cos^(2)((3pi)/(8)) + cos^(2)((5pi)/(8))+ cos^(2)((7pi)/(8))=2

Prove that cos ""(pi)/(9) cos ""( 2pi)/(9) cos "" (3pi)/(9) cos ""(4pi)/(9) = (1)/(2 ^(4)).

Evaluate : cos ""(pi)/(8) sin ""(pi)/(8)

Prove that : cos(pi/7)cos((2pi)/7) cos((3pi)/7)=1/8

Prove that sin ^(2) ((pi)/(8) + (theta)/(2)) - sin ^(2) ((pi)/(8) - (theta)/(2)) = sin ""(pi)/(4) sin theta.

Prove that cos "" (2pi)/(15) cos "" (4pi)/(15) cos "" (8pi)/(15) cos "" (14pi)/(15) = (1)/(16).

Prove that sin^(2) (pi/6) + cos^(2) (pi/3) - tan^(2) (pi/4) = - (1)/(2)

Prove that: sin ((8pi)/3) cos ((23pi)/6)+cos ((13pi)/3) sin ((35pi)/6)=1/2

ICSE-COMPOUND AND MULTIPLE ANGLES -EXERCISE 5 (D)
  1. Prove that (cos A + cos B ) ^(2) +(sin A + sin B) ^(2) = 4 cos ^(2) ((...

    Text Solution

    |

  2. Prove that (cos A - cos B) ^(2) + (sin A - sin B ) ^(2) = 4 sin ^(2) (...

    Text Solution

    |

  3. Prove that: cos ^(4) ""(pi)/(8) + cos ^(4) ""(3pi)/(8) + sin ^(4) "" (...

    Text Solution

    |

  4. sin ^(4) "" (pi)/(8) + sin ^(4) "" (3pi)/(8) + sin ^(4) "" (5pi)/(8) +...

    Text Solution

    |

  5. cos alpha cos(60^(@) - alpha ) cos (60^(@) + alpha ) = 1/4 cos 3 alpha...

    Text Solution

    |

  6. (cos ^(3) alpha - cos 3 alpha )/( cos alpha ) + (sin ^(3)alpha + sin 3...

    Text Solution

    |

  7. cos ^(2) 2 theta - sin ^(2) theta = cos theta . cos 3 theta.

    Text Solution

    |

  8. 1 + (cos 2 theta + cos 6 theta)/(cos 4 theta) = (sin 3 theta)/(sin t...

    Text Solution

    |

  9. Prove that cos ^(3) (x-(2pi)/(3)) + cos ^(3) x + cos ^(3) (x + (2pi)/(...

    Text Solution

    |

  10. (1)/(sin 10^(@)) - (sqrt3)/(cos 10 ^(@)) = 4.

    Text Solution

    |

  11. tan 70^(@) -tan 20^(@) - 2 tan 40^(@) = 4 tan 10 ^(@).

    Text Solution

    |

  12. tan theta + 2 tan 2 theta + 4 tan 4 theta + 8 cot 8 theta = cot theta.

    Text Solution

    |

  13. 4 (cos ^(3) 20^(@) + cos ^(3) 40^(@)) = 3 ( cos 20 ^(@) + cos 40^(@))

    Text Solution

    |

  14. Prove that 4(cos ^(3) 10^(@) + sin ^(3) 20^(@)) = 3 ( cos 10^(@) + sin...

    Text Solution

    |

  15. Prove that cos ^(3) x sin ^(2) x = (1)/(16) (2cos x - cos 3x - cos 5x)...

    Text Solution

    |

  16. cot A + cot (60^(@) + A) + cot (120^(@) +A) = 3 cot 3 A.

    Text Solution

    |

  17. Prove that : cos 36 ^(@) - sin 18^(@) = (1)/(2).

    Text Solution

    |

  18. cos ^(2) 36^(@) + sin ^(2) 18^(@) = (3)/(4).

    Text Solution

    |

  19. 3 cos 72 ^(@) -4 sin ^(3) 18^(@) = cos 36 ^(@).

    Text Solution

    |

  20. cos ^(2) 48^(@) - sin ^(2) 12 ^(@) = (sqrt5+1)/(8).

    Text Solution

    |