Home
Class 11
MATHS
Prove that cos ^(3) x sin ^(2) x = (1)/(...

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

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 sin (n+1) x sin (n +2) x + cos (n +1) x cos (n +2) x = cos x

Prove that: (sin 3 x +sin x) sin x + (cos 3x - cos x) cos x = 0

Prove that (sin 5x - 2 sin 3 x + sin x )/( cos 5 x - cos x ) = tan x

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

(1 + sin 2x + cos 2x )/( cos x + sin x ) = 2 cos x

Prove that : (cos 4x sin 3x - cos 2x sin x)/(sin 4x .sin x + cos 6x .cos x) = tan 2x

Prove that: sin 3x + sin 2x - sin x = 4 sin x cos x/2 cos (3x)/2

Prove that: sin (n + 1) x sin (n + 2)x + cos (n + 1) x cos (n + 2) x = cos x

Prove that : cos ((pi)/(3) + x) = ( cos x - sqrt3 sin x )/(2)

Prove that cos ^(3) (x-(2pi)/(3)) + cos ^(3) x + cos ^(3) (x + (2pi)/(3)) = (3)/(4) cos 3x.

ICSE-COMPOUND AND MULTIPLE ANGLES -EXERCISE 5 (D)
  1. 4 (cos ^(3) 20^(@) + cos ^(3) 40^(@)) = 3 ( cos 20 ^(@) + cos 40^(@))

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. 3 cos 72 ^(@) -4 sin ^(3) 18^(@) = cos 36 ^(@).

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |