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Find the exact value of cos7(pi)/12 using sum and/or difference identities.

  • Trigonometric -

    sometimes it is easier to think in degrees, and then switch back

    7π/12 = 105 degrees and 105 = 60+45
    both angles that we know

    cos 105
    = cos(60+45)
    = cos60cos45 - sin60sin45
    = (1/2)(√2/2) - (√3/2)(√2/2)
    = (√2 - √6)/4

    so cos7π/12 = (√2-√6)/4

  • Trigonometric -

    cos 7π/12

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