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The values of A and theta if (1+sin alph...

The values of A and `theta` if `(1+sin alpha+icosalpha)^8=A(costheta+isintheta)` are respectively

A

A) `2^8cos^8(pi/4-alpha/2),-2alpha`

B

B) `2^8cos3alpha,-3alpha`

C

C) `2^8cos^8(pi/4-alpha/2),-4alpha`

D

D) `2^8cos alpha,-alpha`

Text Solution

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The correct Answer is:
C
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(1-costheta+isintheta)^8 =

(1-costheta+isintheta)^6 =

(1+costheta-isintheta)^4 =

|1+costheta+isintheta|=

(1+costheta-isintheta)^(n)

(1-costheta+isintheta)^(6)

(1-costheta+isintheta)/(1+costheta-isintheta)

If costheta-sintheta=1 , then theta

((1+costheta+isintheta)/(1+costheta-isintheta))^(n)

(1+costheta+isintheta)^(n)+(1+costheta-isintheta)^(n)

AAKASH SERIES-DEMOIVRE'S THEOREM-PRACTICE EXERCISE
  1. (1+i)^(5)+(1-i)^(5)

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  2. If (sinalpha+icosalpha)^4(cos2alpha-isin2alpha)^(-2)=costheta+isinthet...

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  3. The values of A and theta if (1+sin alpha+icosalpha)^8=A(costheta+isin...

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  4. (1-costheta+isintheta)^8=

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  5. (cos75^0+isin75^0)/(cos30^0+isin30^0)=

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  6. If x+1/x=2costheta then x^(10)+(1)/(x^(10))=

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  7. If x satisfies the equation x^2-2xcostheta+1=2costheta,then the value ...

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  8. ((costheta+isintheta)^5(cos3theta-isin3theta)^6)/((cos2theta+isin2thet...

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  9. ((sinpi//8+icospi//8)/(sinpi//8-icospi//8))^(8)

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  10. ((1+sintheta+icostheta)/(1+sintheta-icostheta))^(n)

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  11. If ((sqrt3//2+(1//2)i)/(sqrt3//2-(1//2)i))^(120)=p+iq,then

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  12. If n is a positive integer, then (1+i)^n+(1-i)^n=

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  13. Assertion (A) : (sqrt3+i)^6+(sqrt3-i)^6=-128 Reason (R) : If n is ...

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  14. (sqrt3+i)^7+(sqrt3-i)^7=

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  15. (cos""(pi)/(6)+isin""(pi)/(6))^(1//2)+(cos""(pi)/(6)-isin""(pi)/(6))^(...

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  16. One value of (1+isqrt3)^(3//4)+(1-isqrt3)^(3//4) is equal to

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  17. One of the value of [cos(pi//6)-isin(pi//6)]^(11//2)/[cos(pi//6)+isin(...

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  18. If x=cosalpha+isinalpha,y=cosbeta+isinbeta," then "(x)/(y)+(y)/(x)

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  19. If x=cisalpha,y=cisbeta" then " x^3y^4-(1)/(x^3y^4)=

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  20. If a,b and c are in G.P then (b - a)/(b - c) + (b + a)/(b + c)

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