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If cos alpha+cos beta+cos gamma=0 & sin ...

If `cos alpha+cos beta+cos gamma=0` & `sin alpha +sin beta +sin gamma=0`. Then Prove that
`cos2alpha+cos2beta+cos2gamma=0=sin2alpha+sin2beta+sin2gamma`

A

2

B

1

C

`1/2`

D

0

Text Solution

Verified by Experts

The correct Answer is:
D
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AAKASH SERIES-DEMOIVRE'S THEOREM-EXERCISE -II
  1. The value of 1+sum(k=0)^14{(cos)((2k+1)pi)/(15)+(isin)((2k+1)pi)/(15...

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  2. If alpha and beta are the roots of the equation x^2-2x+4=0...

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  3. If cos alpha+cos beta+cos gamma=0 & sin alpha +sin beta +sin gamma=0. ...

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  4. If cosalpha+cosbeta+cosgamma=0=sin alpha+sinbeta+singamma then cos^2al...

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  5. If cosalpha+cosbeta+cosgamma=0=sinalpha+sinbeta+singamma then cos(2alp...

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  6. If cosalpha+cosbeta+cosgamma=0=sinalpha+sinbeta+singamma then x^(sin(2...

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  7. If cosalpha+coabeta+cosgamma=0=sinalpha+sinbeta+singamma then cos(alph...

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  8. If A+B+C=pi and cosA+cosB+cosC=0=sinA+sinB+sinC then cos3A+cos3B+cos3C...

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  9. If x^6+1=0, then x =

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  10. find the roots x^(11)-x^7+x^4-1=0

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  11. The number of common roots of 15th and of 25th roots of unity are

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  12. The common roots of the equation x^(12)-1=0,x^4+x^2+1=0 are

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  13. The product of all nth roots of unity (n gt 1) is

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  14. The product of the distinct (2n)^(th) roots 1+isqrt3 is

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  15. If alpha is a non real root of x^6=1 then (alpha^5+alpha^3+alpha+1)/(a...

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  16. If 1,alpha1,alpha2,…..alpha(n-1) are the n^(th) roots of unity then (1...

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  17. If 1,alpha1,alpha2,…..alpha(n-1) are the n^(th) roots of unity and n i...

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  18. If alpha is an n^(th) root of unity then prove that 1+2alpha+3alpha^2+...

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  19. Statement-I : ((costheta+isintheta)^5(cos3theta-isin3theta)^6)/((co...

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  20. Statement-I : If xn=cos(pi//2^n)+isin (pi//2^n) then x1.x2.x3…..=-...

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