Sinxcos y = 1/3 (sin (x + y) + sin (x - y)) TRUE OR FALSE

Step-by-step explanation:

false (counter-example) : put x = π/6 and y = π/3

calculate 1) sinxcos y you have : (sinπ/6) (cosπ/3) = (1/2) (1/2) = 1/4

2) 1/3 (sin (x + y) + sin (x - y))

x+y = π/6 + π/3 = π/2

x - y = π/6 - π/3 = - π/6

so : 1/3 (sin (π/2) + sin ( - π/6)) = 1/3 (1 - 1/2) = 1/6 because : sin (π/2) = 1

sin ( - π/6) = - sin (π/6) = - 1/2

but : 1/4 ≠ 1/6