Sin 40 градусов cos 10 градусов - cos 40 градусов sin 10

Предыдущий
вопрос Следующий
вопрос

First, we need to convert the given angles from degrees to radians:

Sin(40 degrees) = Sin(40 π/180) = Sin(2π/9
Cos(10 degrees) = Cos(10 π/180) = Cos(π/18
Cos(40 degrees) = Cos(40 π/180) = Cos(2π/9
Sin(10 degrees) = Sin(10 π/180) = Sin(π/18)

Now we can substitute these values into the expression:

Sin(40°)Cos(10°) - Cos(40°)Sin(10°) = Sin(2π/9)Cos(π/18) - Cos(2π/9)Sin(π/18)

Using the angle addition formula for sine, we get:

Sin(α + β) = Sin(α)Cos(β) + Cos(α)Sin(β)

So,

Sin(2π/9)Cos(π/18) - Cos(2π/9)Sin(π/18) = Sin(2π/9 + π/18) = Sin(13π/18)

Therefore, the value of the expression Sin(40°)Cos(10°) - Cos(40°)Sin(10°) is Sin(13π/18).