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If cosbeta is the geometric mean between...

If `cosbeta` is the geometric mean between `sinalphaa n dcosalpha,` where `0

A

`-2sin^(2)((pi)/(4)-alpha)`

B

`-2cos^(2)((pi)/(4)+alpha)`

C

`2sin^(2)((pi)/(4)+alpha)`

D

`2cos^(2)((pi)/(4)-alpha)`

Text Solution

Verified by Experts

The correct Answer is:
A, B
`2 sin alpha cos alpha=2cos^(2)beta`
`sin2alpha=1+cos 2beta`
`therefore cos 2beta=-(1-sin 2alpha)`
`=-(1-cos((pi)/(2)-2a))`
`=-2sin^(2)((pi)/(4)-alpha))`
`=-2cos^(2)((pi)/(4)+alpha)`
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Knowledge Check

  • The two geometric means between the numbers 1 and 64 are

    A
    1 and 64
    B
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    C
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    D
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  • If H_(1) , H_(2) are two harmonic means between two positive numbers a and b , (a != b) , A and G are the arithmetic and geometric means between a and b , then (H_(2) + H_(1))/(H_(2) H_(1)) is

    A
    `A/G`
    B
    `(2A)/G`
    C
    `A/(2G^(2))`
    D
    `(2A)/G^(2)`

  • If (a^(n + 1) + b^(n + 1))/(a^(n) + b^(n)) is the arithmetic mean between a and b , then n =

    A
    2
    B
    `-2`
    C
    0
    D
    2

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