Use the product-to-sum formula to write the given product as a sum or difference. 12 sin (∏/6) cos (∏/6)

Question

Use the product-to-sum formula to write the given product as a sum or difference.

12 sin (∏/6) cos (∏/6)

Answer 1

pi/6 = 30 degrees

sin30 = 1/2

cos30 = (1/2)sqr3

12sin30cos30 = 12(1/2)(1/2)sqr3 = 3sqr3

so, whatever you come up with using formulas should give you the same answer in the end

one formula is the double angle formula for sines: sin2x = 2sinxcosx

12sinxcosx =6(2sinxcosx) = 6sin2x = 6sin60= 6((1/2)sqr3 = 3sqr3

12sin(pi/6)cos(pi/6) = 6sin(pi/3) = 3sqr3

but you seem to want product to sum formula for sines

sin(A+B) = sinAcosB+ sinBcosA where A=B = pi/6 = 30 degrees

sin60 = sin30cos30 +sin30cos30 = 2sin30cos30 multiply by 6

6sin60 = 12sin30cos30