what is the equivalent identity of (sinA+-sinB)?

Question

please help. . i need the answer now. . thanks

Answer 1

for instance

sin(x+y)=sinx.cosy + cosx.siny

set y=x
gives
sin(2x) = 2*sinx*cosx

so sin(a) + sin(b) = 2*sina/2*cosa/2 + 2*sinb/2*cosb/2

what identity are you looking for ?

Answer 2

What do you mean sinA +- sinB? Do you mean sinA - sinB or sinA + sinB? Please update your question and I'll answer it.

Answer 3

A = (A+B)/2 + (A-B)/2
B = (A+B)/2 - (A-B)/2
sinA = sin[(A+B)/2 + (A-B)/2] = sin[(A+B)/2]cos[(A-B)/2] + cos[(A+B)/2]sin[(A-B)/2]
sinB = sin[(A+B)/2 - (A-B)/2] = sin[(A+B)/2]cos[(A-B)/2] - cos[(A+B)/2]sin[(A-B)/2]
so
sinA + sinB = 2sin[(A+B)/2]cos[(A-B)/2]
similarly
sinA - sinB = 2cos[(A+B)/2]sin[(A-B)/2]