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cosalpha+cosbeta-cos(alpha+beta)=3/2 the...

`cosalpha+cosbeta-cos(alpha+beta)=3/2` then show that `alpha=beta=pi/3`

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

cos(beta-gamma)+cos(gamma-alpha)+cos(alpha-beta)=-3/2 show that cosalpha+cosbeta+cosgamma=0 and sinalpha+sinbeta+singamma=0 also cos(beta-gamma)=cos(gamma-alpha)=cos(alpha-beta)=-1/2 .

Knowledge Check

  • If 0 lt alpha, beta lt pi and cos alpha +cos beta-cos(alpha+beta)=3//2 then sin alpha+cos beta is equal to

    A
    0
    B
    1
    C
    `(sqrt(3)+1)//2`
    D
    `sqrt(3)`

  • if abs({:(sinalpha, cosbeta), (cosalpha, sinbeta):})=1/2 , where alpha, beta are acute angles, then find the value of alpha+beta . a) pi/3 b) (2pi)/3 c) pi/2 d) pi/4

    A
    `pi/3`
    B
    `(2pi)/3`
    C
    `pi/2`
    D
    `pi/4`

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

    If cosalpha+cosbeta=0=s inalpha+s inbeta, then prove that cos2alpha+cos2beta=-2cos(alpha+beta)dot

    If alpha!=beta and atanalpha+b tanbeta=(a+b)tan((alpha+beta)/2) ,then show that (cosalpha)/(cosbeta)=a/b

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

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

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

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