Question

Sinx-2sinx-1+корень 3 sinx+sin4П/3

Answer 1

Объяснение:

Вот решение))))))))))))))))))))))))

Answer 2

To simplify the expression sin(x) - 2sin(x) - 1 + √3sin(x) + sin(4π/3), we can combine like terms:

sin(x) - 2sin(x) + √3sin(x) + sin(4π/3) - 1

Combining the three terms with sin(x), we get:

(1 - 2 + √3)sin(x) + sin(4π/3) - 1

Simplifying the coefficient of sin(x):

(-1 + √3)sin(x) + sin(4π/3) - 1

Now, let's evaluate the remaining trigonometric term sin(4π/3):

sin(4π/3) is equal to sin(2π + π/3), which falls within the third quadrant. In the third quadrant, sin(x) is negative. Also, sin(x) in the third quadrant has the same absolute value as sin(x) in the first quadrant, but with a negative sign. Therefore, sin(4π/3) = -sin(π/3) = -√3/2.

Substituting this value back into the expression, we have:

(-1 + √3)sin(x) - √3/2 - 1

Simplifying further:

(-1 + √3)sin(x) - √3/2 - 2/2

Combining the constants:

(-1 + √3)sin(x) - (2 + √3)/2

So, the simplified expression is (-1 + √3)sin(x) - (2 + √3)/2.