Question

Cos750cos150+sin750sin150

Answer 1

Ответ:

Это формула: cos(750°-150°)

Answer 2

To simplify the expression cos(750)cos(150) + sin(750)sin(150), we can use the trigonometric identity:

cos(A - B) = cos(A)cos(B) + sin(A)sin(B)

Let's rewrite the expression using this identity:

cos(750)cos(150) + sin(750)sin(150) = cos(750 - 150)

Since 750 - 150 = 600, the expression simplifies to:

cos(600)

To evaluate cos(600), we need to convert the angle to a standard angle within the range of 0 to 360 degrees or 0 to 2π radians.

600 degrees is equivalent to 600 - 360 = 240 degrees, or 240 * π/180 = 4π/3 radians.

Now we can find the cosine of 4π/3:

cos(4π/3) = -0.5

Therefore, the simplified value of cos(750)cos(150) + sin(750)sin(150) is -0.5.