Question

Express cos^2x in terms of cos2x

Answer 1

Expressing cos2x in terms of cos2x involves using the double angle cosine identity, which results in cos2x = (cos2x + 1) / 2.

Step-by-step explanation:

To express cos2x in terms of cos2x, we can use a trigonometric identity. The double angle formula for cosine is cos2x = cos2x - sin2x, which can also be written as cos2x = 2cos2x - 1 because sin2x = 1 - cos2x. By rearranging the formula, we get cos2x = (cos2x + 1) / 2.

This derivation shows that the cosine squared of an angle can be represented as half the sum of the cosine of twice that angle and one. This relationship can be useful for simplifying expressions or solving trigonometric equations where a substitution like this might help to reduce complexity.

Answer 2

cos 2x = cos^2 x - sin^2 x
cos^2 x = 1 - sin^2 x
cos 2x = 1 - 2 sin^2 x
sin^2 x = 1/2( 1 - cos 2x)