Question

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

Answer 1

Answer:

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