Question

Решите sin(a+b)-sin(a-b)

Answer 1

sinA*cosB+cosA*sinB+sinA*cosB-cosAsinB=2sinA*cosB

Answer 2

To solve the expression sin(a + b) - sin(a - b), we can use the trigonometric identity for the difference of two sines:

sin(x) - sin(y) = 2 * cos((x + y) / 2) * sin((x - y) / 2)

So, for our expression, let's plug in (a + b) for x and (a - b) for y:

sin(a + b) - sin(a - b) = 2 * cos((a + b + a - b) / 2) * sin((a + b - a + b) / 2)

Now, simplify the expression inside the cosine and sine functions:

cos((a + b + a - b) / 2) = cos(a) (since (a + b) + (a - b) = 2a)

sin((a + b - a + b) / 2) = sin(b) (since (a + b) - (a - b) = 2b)

Now, substitute back into the original expression:

sin(a + b) - sin(a - b) = 2 * cos(a) * sin(b)

So, the final answer is 2 * cos(a) * sin(b).