Solve cos4u = cos^2 2u-sin^2 2u?

1. Solve cos4u = cos^2 2u-sin^2 2u

2. Solve 4 cot 4x = 2 cot 2u - 2 tan 2u

3. Solve cos x = sin 2x, within the interval [0,2pi)

4. Solve cos^2 (x/2) = cos^2 x, within the interval [0,2pi)

5. The position of a weight attached to a spring is s(t) = -9 cos 8pit inches after t seconds. What is the maximum height that the weight reaches above the equilibrium position and when does it first reach the maximum weight

a) the max height of 18 inches is first reached after 2 seconds

b) the max height of 9 inches is first reached after 0.13 seconds

c) the max height of 9 inches is first reached after 4 seconds

d) the max height of 18 inches is first reached after 4 seconds