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[(cos alpha-cos beta)+i(sin alpha-sinbet...

`[(cos alpha-cos beta)+i(sin alpha-sinbeta)]^n+[(cos alpha-cos beta)-i(sin alpha-sin beta)]^n=`

A

`2^(n+1).sin^n((alpha-beta)/(2))cos[(pi/2+(alpha+beta)/(2))]`

B

`2^(n-1).sin^n((alpha-beta)/(2))cos[(pi/2+(alpha+beta)/(2))]`

C

`2^(n+1).sin^n((alpha+beta)/(2))cos[(pi/2+(alpha-beta)/(2))]`

D

`2^(n-1).sin^n((alpha+beta)/(2))cos[(pi/2+(alpha-beta)/(2))]`

Text Solution

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The correct Answer is:
A
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AAKASH SERIES-DEMOIVRE'S THEOREM-EXERCISE -II
  1. If ((1+costheta+isintheta)/(sintheta+i+icostheta))^(4)=cosntheta+isinn...

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  2. ((1+isqrt3)/(1-isqrt3))^6+((1-isqrt3)/(1+isqrt3))^6=

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  3. [(cos alpha-cos beta)+i(sin alpha-sinbeta)]^n+[(cos alpha-cos beta)-i(...

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  4. If (sqrt3+i)^(100)=2^(99)(a+ib) then b=

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  5. If z=costheta+isintheta, then (z^(2n)-1)/(z^(2n)+1)

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  6. If x=cos alpha+i sin alpha,y=cos beta+isinbeta, then (x-y)/(x+y)=

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  7. If x=cos alpha+i sin alpha,y=cos beta+isinbeta, then x/y-y/x=

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  8. If theta=pi/6, then the 10th term of the series 1+(costheta+isintheta)...

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  9. If n is a positive integer and (1+i)^(2n)+(1-i)^(2n)=kcos(npi//2) then...

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  10. If n is positive integer and (1+isqrt3)^n+(1-isqrt3)^n=2^(n+1) cos...

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  11. If alphaandbeta are the roots of x^(2)-2x+4=0" then "alpha^(n)+beta^(n...

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  12. Show that one value of ((1+sin""pi/8+i cos ""pi/8)/(1+sin"" pi/8-i...

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  13. If n is a positive integer, then (a+ib)^(m//n)+(a-ib)^(m//n)

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  14. If p=cos2 alpha+isin2 alpha,q=cos2beta+isin2beta then sqrt(p//q)-sqrt(...

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  15. The values of (1-sqrt3i)^(1//3) are

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  16. The product of the four values of (1/2+i(sqrt3)/(2))^(3//4) is

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  17. Two of the three values of (-1)^(1//3) are cos(pi//3)+isin(pi//3),cos(...

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  18. One value of (1+i)^(1//2) is 2^(1//4)e^(ipi//8).The other value is

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  19. If z+1/z=1 and z be any complex number,then the value of z^(99)+(1)/(z...

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  20. If (sqrt3-i)^n=2^n,b epsilon 1,the set of integers,then n is a multipl...

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