Mastering Trigonometry: The Double-Angle And Half-Angle Identities Of Cosine

cos2x =

1-2sin^2x

Cosine is a trigonometric function that returns the ratio of the adjacent side to the hypotenuse of a right triangle. The notation cos2x indicates that we are taking the cosine of an angle that is twice x.

Using the double-angle identity for cosine, we can rewrite cos2x as:

cos2x = cos(x + x) = cos(x) * cos(x) – sin(x) * sin(x)

Alternatively, we can use the half-angle identity for cosine, which gives us:

cos2x = 2cos^2(x) – 1

Here, we can see that cos2x is a function of cos(x), which is an angle measure. The resulting value will depend on the specific angle x that we plug into the function.

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