Home
Class 12
MATHS
If alpha= (2pi)/(7), then prove that cos...

If `alpha= (2pi)/(7)`, then prove that `cos alpha+ cos 2 alpha+ cos 4alpha=-(1)/(2)`. Hence, deduce that `sin alpha+ sin 2alpha+ sin 4alpha=(sqrt(7))/(2)`

Promotional Banner

Topper's Solved these Questions

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise ALGEBRA|141 Videos

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise COORDINATE GEOMETRY (TWO DIMENSIONAL COORDINATE GEOMETRY)|124 Videos

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise WBJEE 2026|23 Videos

  • METHOD OF SUBSTITUTION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Assertion-Reason Type)|2 Videos

  • ORDER AND DEGREE OF DIFFERENTIAL EQUATION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (E Assertion - Reasion Type )|2 Videos

Similar Questions

Explore conceptually related problems

If alpha=(2pi)/(7) then prove that sin alpha sin 2 sin 4 alpha =-(sqrt(7))/(8)

If alpha=(pi)/(8 n) then prove that sin^(2) alpha+ sin^(2)3 alpha+ sin ^(2) 5 alpha+.. to 2n terms =n.

If alpha =(pi)/(18) radian then the value of (cos alpha + cos 2 alpha+ cos 3 alpha +…+ cos 18 alpha) is-

Prove that, (cos alpha + sin alpha)/(cos alpha -sin alpha)-(cos alpha - sin alpha)/(cos alpha + sin alpha) = 2 tan 2 alpha

Prove that, (sin alpha + cos alpha)/(cos alpha-sin alpha)=tan2 alpha + sec 2 alpha

Prove that, 1/3 ( cos^(3) alpha sin 3 alpha + sin^(3) alpha cos 3 alpha) = 1/4 sin 4 alpha

Prove that, (1+ cos 2 alpha + sin 2 alpha)/(1-cos 2 alpha +sin 2 alpha)=cot alpha

If cos alpha, sin alpha and cot alpha are in G.P. show that tan^(6)alpha- tan^(2)alpha=1

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

Prove that (cos alpha - cos beta)^(2) +(sin alpha - sin beta)^(2) = 4 "sin"^(2) (alpha-beta)/2

CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-TRIGONOMETRY
  1. Show that 3(sin x- cos x)^(4)+4 (sin ^(6)x+cos^(6)x)+ 6(sin x+cos x)^(...

    Text Solution

    |

  2. Show that 1+cos 56^(@)+ cos 58^(@)-cos66^(@)=4 cos 28^(@) cos 29^(@...

    Text Solution

    |

  3. If alpha= (2pi)/(7), then prove that cos alpha+ cos 2 alpha+ cos 4alph...

    Text Solution

    |

  4. In any triangle ABC if sin A sin B sin C+ cos A cos B=1, then show tha...

    Text Solution

    |

  5. If sin theta+ sin phi= sqrt(3)( cos phi- cos theta), then show that si...

    Text Solution

    |

  6. Prove that : tan 70^(@)+ tan 10^(@)- tan 50^(@)= sqrt(3)

    Text Solution

    |

  7. Prove that : 4 sin 50^(@)- sqrt(3) tan 50^(@)=1

    Text Solution

    |

  8. If alpha, beta , gamma lengths of the altitudes of a triangle ABC, pro...

    Text Solution

    |

  9. If a sin theta+ b cos theta=0,then find theta

    Text Solution

    |

  10. If cos^(3) theta = kcos (alpha- 3 theta) and sin ^(3) theta= ksin (alp...

    Text Solution

    |

  11. Show that the general solution of sin x- 3 sin 2x+sin 3x= cos x-3 cos ...

    Text Solution

    |

  12. If k is a positive integer, show that 2[ cos x+ cos 3x+ cos 5x+ ..+ ...

    Text Solution

    |

  13. If alpha=(pi)/(8 n) then prove that sin^(2) alpha+ sin^(2)3 alpha+ sin...

    Text Solution

    |

  14. If sin A+ tan A= a and cos A+ cot A= b, then show that (1+a)^(-2)+(1...

    Text Solution

    |

  15. If a^(2)(1- sin theta) +b^(2)(1+ sin theta)= 2 ab cos theta then show ...

    Text Solution

    |

  16. Show that (1+ sin A)/(cosA)+( cos B)/(1- sin B)=(2 (sin A- sin B))/(...

    Text Solution

    |

  17. If n is positive integer and "cos" (pi)/(2n)+"sin" (pi)/(2n) =(sqrt(n)...

    Text Solution

    |

  18. Solve : sec theta+"cosec" theta=2 sqrt(2)

    Text Solution

    |

  19. Solve : tan^(3) theta+ cot^(3) theta= 8 "cosec"^(3) 2 theta+12

    Text Solution

    |

  20. Solve : ("sin" (x)/(2) "cos" (x)/(2))/(1-8 "sin"^(2)(x)/(2) "cos"^(2...

    Text Solution

    |