ЯсноПонятно24

To simplify this expression, we can expand the left side using the distributive property:

(sinx)(√3siny) + (sinx)(cosy) - (cosx)(√3siny) - (cosx)(cosy)

Now, we can use the trigonometric identities sin(α)cos(β) = (1/2)(sin(α+β) + sin(α-β)) and cos(α)cos(β) = (1/2)(cos(α+β) + cos(α-β)) to simplify further:

(1/2)(sin(x+y) + sin(x-y))√3 + (1/2)(sin(x+y) - sin(x-y))cosy - (1/2)(cos(x+y) + cos(x-y))√3 - (1/2)(cos(x+y) - cos(x-y))cosy

Now, we can simplify further:

(1/2)(√3sin(x+y) + sin(x-y) - √3cos(x+y) - cos(x-y)) = 2√2

Therefore, the simplified expression is:

√3sin(x+y) + sin(x-y) - √3cos(x+y) - cos(x-y) = 4√2