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cos ( theta + alpha)* cos ( theta - alph...

`cos ( theta + alpha)* cos ( theta - alpha) + sin ( theta + alpha) * sin (theta - alpha )=`

A

`cos 2alpha `

B

`sin 2 alpha `

C

`cot 2 alpha `

D

`tan 2 alpha `

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • If sin ( theta + alpha ) = cos ( theta + alpha ) , then tan theta =

    A
    `(1+ tan alpha)/(1- tan alpha ) `
    B
    `(1- tan alpha )/(1+ tan alpha ) `
    C
    `(tan alpha )/(1 + tan alpha )`
    D
    `(tan alpha )/(1- tan alpha )`

  • If a* cos ( theta + alpha ) = b cos ( theta - alpha ) , " then " ( a+ b) tan theta =

    A
    `(a+ b) cot alpha `
    B
    `(a-b) cot alpha `
    C
    `(a+b) cot beta `
    D
    `(a-b) cot beta `

  • If alpha + beta + gamma = 2 theta , " then " cos theta + cos ( theta - alpha ) + cos (theta - beta ) + cos ( theta - gamma ) =

    A
    `4 sin""(alpha)/(2)* cos""(beta)/(2) * sin""(gamma)/(2) `
    B
    `4 cos""(alpha)/(2) cos""(beta)/(2) cos""(gamma)/(2) `
    C
    `4 sin""(alpha)/(2) * sin""(beta)/(2) * sin""(gamma)/(2) `
    D
    `4 sin alpha * sin beta * sin gamma `

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