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x = cos 55^(@), y = cos 65^(@), z= cos 1...

`x = cos 55^(@), y = cos 65^(@), z= cos 175^(@) " then " xy+yz+ zx=`

A

`-3/4`

B

`3/4`

C

`3/2`

D

`1/2`

Text Solution

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The correct Answer is:
A
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x = cos 55^(@) , y = cos 65^(@) , z = cos 175^(@) implies xy + yz + zx =

cos5^(@) + cos 24^(@) + cos 175^(@) + cos 204^(@) + cos 300^(@) =

Knowledge Check

  • cos 25^(@) - cos65^(@) =

    A
    `sqrt(2) cos 20^(@) `
    B
    `sqrt(2) sin 20^(@) `
    C
    `sqrt(3) cos 20^(@) `
    D
    `sqrt(3) sin 20^(@) `

  • If x=cos 1 , y= cos1^(@) then

    A
    `x=y`
    B
    `x lt y `
    C
    `x gt y`
    D
    none

  • If cos ^(-1) x + cos ^(-1) y + cos ^(-1) z = 2pi, then

    A
    `x + y+ z - 3=0`
    B
    `x +y+ z + 3=0`
    C
    `x + 2y + 3z -5=0`
    D
    `x-y-z=0`

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    Explore conceptually related problems

    Statementj - I , If x cos theta = y cos (120^(@) + theta) = z cos ( theta + 240^(@)) then xy + yz + zx = 1 Statement - II : cos alpha + cos (120^(@) + alpha) + cos (120^(@) - alpha) = 0 Which of the above statements is correct

    I : If x cos theta = y cos (120^@ + theta ) = z cos ( theta + 240^(@)) then xy+ yz+ zx=1 II : cos alpha + cos (120^(@) + alpha ) + cos (120^@ - alpha ) =0

    If cos^(-1) x + cos^(-1) y + cos^(-1) z = 3pi , then

    (sin 65^(@) + sin 25^(@))/( cos 65^(@) + cos 25^(@))=

    Statement-I: If x cos theta = y cos(120^(@) + theta) = zcos(theta + 240^(@)) , then xy + yz + xz=0 Statement II: If cosalpha + cos(120^(@) + alpha) + cos(120^(@)-alpha)=0 Then which of the above statements is/are correct ?

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