Understanding and Simplifying the Cosine of Twice an Angle | The Double-Angle Formula for Cosine

cos 2x

The term “cos 2x” refers to the cosine of twice the angle x

The term “cos 2x” refers to the cosine of twice the angle x. In trigonometry, the cosine function is a mathematical function that relates the ratio between the adjacent side and the hypotenuse of a right triangle.

To find the value of cos 2x, we can utilize a trigonometric identity called the double-angle formula for cosine:

cos 2x = cos^2(x) – sin^2(x)

This formula states that the cosine of twice an angle is equal to the square of the cosine of the angle minus the square of the sine of the angle.

Using this formula, we can simplify the expression cos 2x further, by using other trigonometric identities:

cos 2x = cos^2(x) – sin^2(x)
= (1 – sin^2(x)) – sin^2(x) (by using the identity cos^2(x) = 1 – sin^2(x))
= 1 – 2sin^2(x)

Therefore, cos 2x can be expressed as 1 – 2sin^2(x).

It’s important to note that this expression represents a new function of sin(x), rather than a simple multiplication or division of sin(x).

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