12cos2u
12cos2u is a trigonometric expression that can be simplified using trigonometric identities. The expression consists of a coefficient, 12, multiplied by the cosine of an angle, 2u. The angle 2u is twice the angle u, which is a common scenario in trigonometry where double-angle identities are applied.
The double-angle identity for cosine states that cos(2u) = cos^2(u) - sin^2(u). However, in the case of 12cos2u,
This expression can be further simplified using the Pythagorean identity, which states that sin^2(u) + cos^2(u) = 1.
Therefore, 12cos2u is equivalent to 24cos^2(u) - 12. This simplification can be useful in various mathematical and