Understanding the Power to Double Angle Formula | Expressing cos^2x in Terms of cos(2x)

cos^2x (Power to Double Angle)

When we see the expression cos^2x, it refers to taking the cosine of x and squaring the result

When we see the expression cos^2x, it refers to taking the cosine of x and squaring the result. In other words, cos^2x is equivalent to (cos(x))^2.

Now, the “power to double angle” formula in trigonometry allows us to express a trigonometric function of a double angle in terms of the original function. For cos^2x, applying the power to double angle formula means rewriting it using the cosine of double the angle x.

The power to double angle formula for cosine is as follows:

cos(2x) = 2cos^2x – 1

To understand this formula, we can break it down:
– The left side, cos(2x), represents the cosine function of the double angle 2x.
– The right side, 2cos^2x – 1, expresses the double angle cosine in terms of the original angle cosine.

By rearranging the formula, we can isolate cos^2x:

2cos^2x = cos(2x) + 1

Finally, if we divide both sides by 2, we obtain the desired expression for cos^2x:

cos^2x = (1 + cos(2x))/2

This is the power to double angle formula for cos^2x. It allows us to find the value of (cos(x))^2 in terms of the cosine of the double angle (2x).

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