# 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.

### 2 Answers

- 1 month agoFavourite 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

- Anonymous1 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