Home
Class 11
MATHS
If cosalpha+cosbeta+cosgamma=0 a n d a...

If `cosalpha+cosbeta+cosgamma=0 a n d a l so sinalpha+sinbeta+singamma=0,` then prove that `cos2alpha+cos2beta+cos2gamma` `=sin2alpha+sin2beta+sin2gamma=0` `sin3alpha+sin3beta+sin3gamma=3sin(alpha+beta+gamma)` `cos3alpha+cos3beta+cos3gamma=3cos(alpha+beta+gamma)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise All Questions|365 Videos

  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|1344 Videos

Similar Questions

Explore conceptually related problems

If cos alpha + cos beta + cos gamma = 0 and also sin alpha + sin beta + sin gamma= 0, then prove that: cos 3 alpha + cos 3beta + cos 3gamma = 3 cos (alpha + beta + gamma)

If cos alpha+cos beta+cos gamma=0=sin alpha+sin beta+sin gamma , then (sin3alpha+sin3beta+sin3gamma)/(sin(alpha+beta+gamma)) is equal to

If sin alpha+ sin beta+ sin gamma=3, then sin^3alpha+sin^3beta+sin^3 gamma=

If cosalpha+cosbeta+cosgamma=0 , then prove that cos3alpha+cos3beta+cos3gamma=12cosalphacosbetacosgamma

If alpha+beta+gamma=pi , prove that : cos^2 alpha + cos^2 beta + cos^2 gamma+2cosalpha cosbeta cosgamma=1 .

If cos(alpha-beta)+cos(beta-gamma)+cos(gamma-alpha)=-3/2 , prove that cosalpha+cosbeta+cosgamma=sinalpha+sinbeta+singamma=0

Given alpha+beta-gamma=pi, prove that sin^2alpha+sin^2beta-sin^2gamma=2sinalphasinbetacosgammadot

If alpha,beta,gamma, in (0,pi/2) , then prove that (s i(alpha+beta+gamma))/(sinalpha+sinbeta+singamma)<1

If cosalpha+cosbeta=0=sinalpha+sinbeta , then prove that cos2alpha +cos2beta=-2cos(alpha +beta) .

If cosalpha+2cosbeta+3cosgamma=sinalpha+2sinbeta+3singamma=0 , then the value of sin3alpha+8sin3beta+27sin3gamma is sin(a+b+gamma) b. 3sin(alpha+beta+gamma) c. 18"sin"(alpha+beta+gamma) d. sin(alpha+2beta+3)

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If the roots of the cubic equation, x^3+a x^2+b x+c=0 are three consec...

    Text Solution

    |

  2. If z1, z2 in C ,z1^2+z2^2 in R ,z1(z1^2-3z2^2)=2 and z2(3z1^2-z2^2)...

    Text Solution

    |

  3. If cosalpha+cosbeta+cosgamma=0 a n d a l so sinalpha+sinbeta+singamm...

    Text Solution

    |

  4. If x+y+z=12 andx^2+y^2+z^2=96 and 1/x+1/y+1/z=36 , then the value x^3+...

    Text Solution

    |

  5. Prove that (1+i)^n+(1-i)^n=2^((n+2)/2).cos((npi)/4), where n is a pos...

    Text Solution

    |

  6. The set {R e((2i z)/(1-z^2)): zi sacom p l e xnu m b e r ,|z|=1,z=+-1}...

    Text Solution

    |

  7. If the equation x^2+ax+bc=0" and " x^2-bx+ca=0 have a common root, the...

    Text Solution

    |

  8. If a r g["z"1("z"3-"z"2)]="a r g"["z"3("z"2-"z"1)] , then find prove t...

    Text Solution

    |

  9. If x" - "i y" "=sqrt((a-i b)/(c-i d)) prove that (x^2+y^2)^2=(a^2+b^2...

    Text Solution

    |

  10. If x^3+3x^2-9x+c is of the form (x-alpha)^2(x-beta) , then c is equ...

    Text Solution

    |

  11. If x=a+b,y=a alpha+b beta and z=abeta+ b alpha , where alpha and beta...

    Text Solution

    |

  12. If z=(a+ib)^5+(b+ia)^5 then prove that Re(z)=Im(z), where a,b in R.

    Text Solution

    |

  13. If a and b are positive numbers and eah of the equations x^2+a x+2b=0 ...

    Text Solution

    |

  14. The real values of xa n dy for which the following equation is satisfi...

    Text Solution

    |

  15. The three angular points of a triangle are given by Z=alpha, Z=beta,Z=...

    Text Solution

    |

  16. Suppose a ,b ,c are the roots of the cubic x^3-x^2-2=0. Then the value...

    Text Solution

    |

  17. Prove that x^3 + x^2 + x is factor of (x+1)^n - x^n -1 where n is odd ...

    Text Solution

    |

  18. If alpha,beta,gamma,delta are four complex numbers such that gamma/del...

    Text Solution

    |

  19. If ax^(2)+(b-c)x+a-b-c=0 has unequal real roots for all c epsilonR, th...

    Text Solution

    |

  20. If z1^2+z2^2-2z1.z2.costheta= 0 prove that the points represented by ...

    Text Solution

    |