The expression equivalent to sin 3x + sin x is 2 cos x cos 2x.
The expression equivalent to sin 3x− sin x is 2 sin x cos 2x.
These are equations that relate the sine, cosine, and tangent functions of one or more angles.
The sum-to-product trigonometric identity states that the sum of two sines can be expressed as the product of two cosines:
sin(x)+sin(y)=2cos(
)cos(
)
We can rewrite the expression in the first drop-down menu as:
sin(3x)+sin(x)=2cos (
) cos (
)
Simplifying the expression, we get:
2cos(x)cos(2x)
Therefore, the correct answer for the first drop-down menu is 2cosxcos2x.
The difference-to-product trigonometric identity states that the difference of two sines can be expressed as the product of two sines:
sin(x)−sin(y)=2sin (
) cos (
)
We can rewrite the expression in the second drop-down menu as:
sin(3x)−sin(x)=2sin (
) cos (
)
Therefore, the correct answer for the second drop-down menu is 2sinxcos2x.