Question

Sin x + sin 2x + sin 3x + sin 4x​

Answer 1

Sin10x ¿¿¿¿¿¿¿¿ не знаю как по другому

Answer 2

X это как 1 теперь всё считаем и получается 10 sin

Answer 3

To simplify the expression sin(x) + sin(2x) + sin(3x) + sin(4x), you can use some trigonometric identities to combine the terms. Here's how you can do it:

1. Use the sum-to-product trigonometric identity:

   sin(A) + sin(B) = 2 * sin((A + B)/2) * cos((A - B)/2)

2. Apply this identity to your expression:

   sin(x) + sin(2x) = 2 * sin((x + 2x)/2) * cos((x - 2x)/2) = 2 * sin(3x/2) * cos(-x/2)

3. Use the identity sin(-x) = -sin(x):

   cos(-x/2) = cos(x/2)

4. Now the expression becomes:

   2 * sin(3x/2) * cos(x/2) + sin(3x) + sin(4x)

5. Apply the sum-to-product identity to sin(3x) + sin(4x):

   sin(3x) + sin(4x) = 2 * sin((3x + 4x)/2) * cos((3x - 4x)/2) = 2 * sin(7x/2) * cos(-x/2) = 2 * sin(7x/2) * cos(x/2)

6. Now, the entire expression becomes:

   2 * sin(3x/2) * cos(x/2) + 2 * sin(7x/2) * cos(x/2)

7. Factor out the common term of 2 * cos(x/2):

   2 * cos(x/2) * (sin(3x/2) + sin(7x/2))

So, the simplified expression is:

2 * cos(x/2) * (sin(3x/2) + sin(7x/2))