Home
Class 11
MATHS
Prove that : cos 36 ^(@) - sin 18^(@) = ...

Prove that : `cos 36 ^(@) - sin 18^(@) = (1)/(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

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

Prove that sin 36^(@) + cos 36^(@) = sqrt(2) cos 9^(@)

Prove that : cos^(4) A - sin^(4) A = 2 cos^(2) A - 1

Prove that sin 36 ^(@) + cos 36 ^(@) = sqrt2 cos 9^(@).

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

Prove that : cos (2 sin^(-1) x) = 1-2x^2

Prove that : (cos ^(2) A + tan ^(2) A - 1 )/( sin ^(2) A ) = tan ^(2) A .

Prove that: cos 18^0 - sin 18^0 = sqrt(2) sin 27^0

Prove that: cos 18^0 - sin 18^0 = sqrt(2) sin 27^0

Prove that sin 12^(@) sin18^(@)sin42^(@) sin48^(@) sin 72^(@) sin78^(@)=(cos18^(@))/(32) .

ICSE-COMPOUND AND MULTIPLE ANGLES -EXERCISE 5 (D)
  1. Prove that cos ^(3) x sin ^(2) x = (1)/(16) (2cos x - cos 3x - cos 5x)...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  5. 3 cos 72 ^(@) -4 sin ^(3) 18^(@) = cos 36 ^(@).

    Text Solution

    |

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

    Text Solution

    |

  7. Prove that sin "" (1)/(10) pi cos ""(1)/(5) pi = (1)/(4).

    Text Solution

    |

  8. sec 72 ^(@) - sec 36^(@) = 2.

    Text Solution

    |

  9. sin ^(2) 24 ^(@) - sin ^(2) 6^(@) = (sqrt5 -1)/(8).

    Text Solution

    |

  10. sin 12 ^(@) sin 48^(@) sin 54 ^(@) = (1)/(8).

    Text Solution

    |

  11. Prove that 4 cos 6^(@) cos 42 ^(@) cos 66^(@) cos 78^(@) = (1)/(4).

    Text Solution

    |

  12. sin "" (pi)/(5) sin "" (2pi)/(5) sin ""(4pi)/(5) sin""(3pi)/(5) = (5)/...

    Text Solution

    |

  13. Prove that cos "" (2pi)/(15) cos "" (4pi)/(15) cos "" (8pi)/(15) cos "...

    Text Solution

    |

  14. cos ^(2) ""(pi)/(10) + cos ^(2) ""(2pi)/(5) + cos^(2) ""(3pi)/(5) + co...

    Text Solution

    |

  15. tan 6 ^(@) tan 42 ^(@) tan 66 ^(@) tan 78^(@) =1

    Text Solution

    |

  16. cos alpha cos 2 alpha cos 4 alpha cos 8 alpha = (1)/(16), if alpha =...

    Text Solution

    |

  17. cos 12 ^(@) cos 24 ^(@) cos 36 ^(@) cos 48^(@) cos 72^(@) cos 84^(@) =...

    Text Solution

    |

  18. If theta = (pi)/(2 ^(n) +1) prove that 2 ^(n) cos theta cos 2 theta c...

    Text Solution

    |

  19. If tan "" (x-y)/( 2 ), tan z, tan "" (x + y)/( 2) are in G.P. then sho...

    Text Solution

    |

  20. If sin theta is G.M. of sin phi and cos phi, then prove that cos 2 th...

    Text Solution

    |