Question

sin(a-b) = sinacosb+cosasinb for all values of a and b. True or false?

Answer 1

False.

Answer 2

evidence?

Answer 3

It should be sin(a - b) = sin(a)cos(b) - cos(a)sin(b)

Answer 4

Let's do it this way to evidence more:
sin(a - b) = sin(a)cos(b) - sin(b)cos(a)
sin(a + b) = sin(a)cos(b) + sin(b)cos(a)
SO,
cos(a - b) = cos(a)cos(b) + sin(a)sin(b)
cos(a + b) = cos(a)cos(b) - sin(a)sin(b)
Simple.

Answer 5

Thank you @Praja_01

Answer 6

Thank you very much @Spectrum.