Verify:cos(360degrees-x)=cos x
To verify the given equation, we can use one of the trigonometric identities:
cos (θ - φ) = cos θ cos φ + sin θ sin φ
We substitute θ with 360 degrees and φ with x:
cos (360 degrees - x) = cos 360 degrees cos x + sin 360 degrees sin x
Now, let's consider the values of cos 360 degrees and sin 360 degrees.
In trigonometry, cos 360 degrees = 1 and sin 360 degrees = 0. This is because the cosine function has a period of 360 degrees, and after 360 degrees, it repeats its values. Similarly, the sine function has a period of 360 degrees and repeats its values as well. Since cos(360 degrees) = 1 and sin(360 degrees) = 0, we can simplify the equation:
cos (360 degrees - x) = 1 * cos x + 0 * sin x
cos (360 degrees - x) = cos x + 0
cos (360 degrees - x) = cos x
Therefore, we have verified that cos(360 degrees - x) = cos x.