## cos 2x

### cos^2 x – sin^2 x

The expression cos 2x involves the cosine of twice the angle x. To find the value of this expression, we can use one of the double angle formulas for cosine, which states that:

cos 2x = cos^2 x – sin^2 x

or

cos 2x = 2cos^2 x – 1

Both of these formulas are equivalent and can be used depending on which one is more convenient in a given situation.

Let’s say that we want to find the value of cos 2x for a specific value of x, let’s say x = 30 degrees. We can use the first formula above, since we know the values of cosine and sine of 30 degrees (which are equal to square root of 3 over 2 and 1/2, respectively). So, we have:

cos 2(30) = cos^2 30 – sin^2 30

cos 60 = (sqrt(3)/2)^2 – (1/2)^2

cos 60 = 3/4 – 1/4

cos 60 = 1/2

Therefore, cos 2x for x = 30 degrees is equal to 1/2.

In general, the value of cos 2x will depend on the value of x and will range between 1 and -1.

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