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Simplify ((cos2theta+isin2theta)^6(c...

Simplify
`((cos2theta+isin2theta)^6(cos3theta+isin3theta)^(-5))/((cos5theta+isin5theta)^(-8)(cos6theta-isin6theta)^(-2))`

Text Solution

Verified by Experts

The correct Answer is:
`cis(25theta)`
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((cos2theta+isin2theta)^(3)(cos3theta-isin3theta)^(4))/((cos3theta+isin3theta)^(2)(cos4theta+isin4theta)^(-3))

((costheta+isintheta)^(5)(cos3theta-isin3theta)^(6))/((cos2theta+isin2theta)^(3)(cos4theta-isin4theta)^(5))

Knowledge Check

  • ((costheta+isintheta)^5(cos3theta-isin3theta)^6)/((cos2theta+isin2theta)^3(cos4theta-isin4theta)^5)=

    A
    1
    B
    `cis(theta)`
    C
    i
    D
    -1

  • Statement-I : ((costheta+isintheta)^5(cos3theta-isin3theta)^6)/((cos2theta+isin2theta)^3(cos4theta-isin4theta)^5)=1 Statement-II : ((cos2theta+isin2theta)^3(cos3theta-isin3theta)^4)/((cos3theta+isin3theta)^2(cos4theta+isin4theta)^(-3))=1

    A
    Only I is true
    B
    Only II is true
    C
    Both I and II are true
    D
    Neither I nor II are true

  • (cos theta + sin theta )^(2) + (cos theta - sin theta )^(2) =

    A
    0
    B
    1
    C
    2
    D
    `sqrt(2)`

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    4 sin 5 theta cos 3 theta sin 2 theta

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