Home
Class 11
MATHS
Prove that sin (n+1) x sin (n +2) x + co...

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

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMPOUND AND MULTIPLE ANGLES

    ICSE|Exercise EXERCISE 5 (D) |60 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)A sin(n+2)A+cos(n+1)A cos(n+2)A=cos A

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

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

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

Prove that sin^(-1) cos (sin^(-1) x) + cos^(-1) x) = (pi)/(2), |x| le 1

sin(n+1)xsin(n+2)x+cos(n+1)xcos(n+2)x=cosx

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

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

Prove that Sigma_(K=0)^(n) ""^nC_(k) sin K x cos (n-K)x = 2^(n-1) sin x.

Prove that sum_(r=0)^(n) ""^(n)C_(r )sin rx. cos (n-r)x = 2^(n-1) xx sin nx .

ICSE-COMPOUND AND MULTIPLE ANGLES -CHEPTER TEST
  1. Show that tan 75^(@) = (sqrt3) +(1 )/( sqrt3 -1) = 2 + sqrt3. Hence de...

    Text Solution

    |

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

    Text Solution

    |

  3. if A+ B + C = pi, and cos A = cos B cos C, show that 2 cot B cot C=1.

    Text Solution

    |

  4. Show that (sin (alpha + beta))/( sin (alpha + beta)) = 2, given that ...

    Text Solution

    |

  5. Show that ( cos 10^(@) + sin 10 ^(@))/( cos 10^(@) - sin 10 ^(@)) = ta...

    Text Solution

    |

  6. If sin 2 A = 4/5, find the value of tan A, (0^(@) le A le (pi)/(3))

    Text Solution

    |

  7. Express cot A in terms of cos 2 A

    Text Solution

    |

  8. Write cos 4 theta in terms of cos theta.

    Text Solution

    |

  9. A positive acute angle is divided into two parts whose tangents are 1/...

    Text Solution

    |

  10. Show that cos 10^(@) + cos 110^(@) + cos 130^(@) = 0

    Text Solution

    |

  11. Show that (sin 5 A + 2 sin 8A + sin 11 A)/( sin 8A + 2 sin 11 A + sin ...

    Text Solution

    |

  12. Show that (1)/(2 sin 10^(@)) - 2 sin 70^(@) =1.

    Text Solution

    |

  13. Show that sin 19^(@) + sin 41^(@) + sin 83^(@) = sin 23 ^(@) + sin 37^...

    Text Solution

    |

  14. If sin A = (1)/(sqrt3) and sin B = (1)/(sqrt5) find the value of tan...

    Text Solution

    |

  15. If sin theta = n sin ( theta + 2 alpha ) , show that ( n -1) tan (the...

    Text Solution

    |

  16. If tan "" (alpha )/(2) and tan "" (beta)/( 2) are the roots of the eq...

    Text Solution

    |

  17. Prove that ((cos A + cos B)/( sin A - sin B )) ^(n) + ((sin A + sin B ...

    Text Solution

    |

  18. Find sin ""(x)/(2), cos "" (x)/(2) and tan "" (x)/(2) in each of the c...

    Text Solution

    |

  19. Find sin ""(x)/(2), cos "" (x)/(2) and tan "" (x)/(2) in each of the c...

    Text Solution

    |

  20. Prove that cos 6x = 32 cos ^(6) x - 48 cos ^(4) x + 18 cos ^(2) x -1.

    Text Solution

    |