Question

Verify using sum &difference identities:

sin(x+y)-sin(x-y)=2cosxsiny

Answer 1

sin(x+y)-sin(x-y)
sinxcosy+cosxsiny-sinxcosy+cosxsiny
sinxcosy -sinxcos+cosxsiny+cosxsiny
=2cosxsiny

Answer 2

Just to provide another method:
sinA-sinB = 2cos[(A+B)/2]sin[(A-B)/2]
Put A=x+y B=x-y into the above formula
sin(x+y)-sin(x-y) = 2cos{(x+y)+(x-y)]/2}sin{(x+y)-(x-y)]/2}
= 2 cos (2x/2) sin (2y/2)
= 2cosxsiny

Answer 3

@alexwee123 what did u do on the third step?

Answer 4

i arranged the values so it can be clear that sinxcosy -sinxcosy would be cancelled out

Answer 5

ok thx ^^