Double Angle Formula.
If the double angle formula for cos2(u) = 2cos^2(u)-1, then write the double angle formula for cos2(u) in terms of sine.
you should write it this way:
cos (2u) = 2cos^2 (u) - 1
but we know cos^2 u = 1 - sin^2 u
so cos (2u) = 2(1 - sin^2 u) - 1
= 2 - 2sin^2 u - 1
= 1 - 2sin^2 u
ohhhhh, i see!
thank you for making it simple to understand
To derive the double angle formula for cos(2u) in terms of sine, we can start with the given formula:
cos(2u) = 2cos^2(u) - 1
Now, let's express the cosine function in terms of sine using the Pythagorean identity:
cos^2(u) = 1 - sin^2(u)
We substitute this expression back into the original formula:
cos(2u) = 2(1 - sin^2(u)) - 1
Simplifying further:
cos(2u) = 2 - 2sin^2(u) - 1
cos(2u) = 1 - 2sin^2(u)
Hence, the double angle formula for cos(2u) in terms of sine is:
cos(2u) = 1 - 2sin^2(u)