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Find the value of cos""(pi)/(12)(sin""...

Find the value of
`cos""(pi)/(12)(sin""(5pi)/(12)+cos""(pi)/(4))+sin""(pi)/(12)(cos""(5pi)/(12)-sin""(pi)/(4))`.

Text Solution

Verified by Experts

The correct Answer is:
`3//2`
`cos15^(@)(sin75^(@)+cos45^(@))+sin15^(@)(cos75^(@)-sin45^(@))`
`=sin(75^(@)+15^(@))+cos(45^(@)+15^(@))=1+(1)/(2)=(3)/(2)`
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Knowledge Check

  • tan""(pi)/(8)tan""(pi)/(12)tan""(3pi)/(8)tan""(5pi)/(12)-sin^(2)""(pi)/(6)=?

    A
    `(1)/(2)`
    B
    `(2-sqrt(3))/(2)`
    C
    `(1)/(4)`
    D
    `(3)/(4)`

  • sin"" (pi)/(4) cos"" (pi)/(12) - cos"" (pi)/(4) sin"" (pi)/(12) is equal to

    A
    `(1)/( sqrt3)`
    B
    `sqrt3`
    C
    `(sqrt3)/(2)`
    D
    `(1)/(2)`

  • sin ""(pi)/(4) cos ""(pi)/(12) - cos ""(pi)/(4) sin ""(pi)/(12) is equal to

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

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