SUM-TO-PRODUCT FORMULA?

SUM-TO-PRODUCT FORMULA

Solve: cos(pi/12) - sin(pi/12)

There is no SUM-TO-PRODUCT FORMULA for this subtraction. 

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  • Favourite answer

    cos(pi/12) - sin(pi/12) =>

    cos(4pi/12 - 3pi/12) - sin(4pi/12 - 3pi/12) =>

    cos(pi/3 - pi/4) - sin(pi/3 - pi/4) =>

    cos(pi/3)cos(pi/4) + sin(pi/3)sin(pi/4) - (sin(pi/3)cos(pi/4) - sin(pi/4)cos(pi/3)) =>

    cos(pi/3)cos(pi/4) + sin(pi/3)sin(pi/4) - sin(pi/3)cos(pi/4) + cos(pi/3)sin(pi/4) =>

    (1/2) * (sqrt(2)/2) + (sqrt(3)/2) * (sqrt(2)/2) - (sqrt(3)/2) * (sqrt(2)/2) + (1/2) * (sqrt(2)/2) =>

    sqrt(2)/2

  • Anonymous
    1 month ago

    cos(A+B) = cos(A)cos(B) – sin(A)sin(B) (equation 1)

    Let  A = π/12 and B = π/4

    Note that sin(π/4) = cos(π/4) = 1/√2. Equation 1 becomes:

    cos( π/12 +  π/4) = cos(π/12)/√2 – sin(π/12)/√2

    . . . . . . . . . . . . . . = (cos(π/12) – sin(π/12))/√2

    Rearranging and using π/12 + π/4 =  π/3 gives:

    cos(π/12) – sin(π/12) = √2cos( π/3)

    . . . . . . . . . . . . . . . . . .= √2/2

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