several questions (f4 maths)

1. {[2(5)^(1/2) + 5]^(1/2) - [-2(5)^(1/2) + 5]^(1/2)} / 4
= {[5 + 2(5)^(1/2)]^(1/2) - [5 - 2(5)^(1/2)]^(1/2)} / 4
=（{[5 + 2(5)^(1/2)]^(1/2) - [5 - 2(5)^(1/2)]^(1/2)}^2(1/2) / 4
=（ {[5 + 2(5)^(1/2)] - 2{[5 + 2(5)^(1/2)][5 - 2(5)^(1/2)]}^(1/2) + [5 - 2(5)^(1/2)] ）^(1/2) / 4
= {10 - 2[5^2 - (2^2)(5)]^(1/2) / 4
= [10 - 2(5)^(1/2)]^(1/2) / 4

2. Period of sin(x) = 2π
Period of sin(x/2) = 2π/(1/2) = 4π

In fact, period of common trigonometric function i.e. sin(x), cos(x), tan(x), sec(x), csc(x) and cot(x) is found by graph and memorable...
Period of sin(x), cos(x), csc(x), sec(x) = 2π
Period of tan(x), cot(x) = π

Furthermore:
F(x) = Asin(Bx + C) + D
A multiplies the altitude of the graph F(x)
B determines the period of the graph F(x)
C shifts the graph F(x) left or right
D shifts the graph F(x) up or down

Period of Asin(Bx + C) + D = 2π/B

In case F(x) = sin(x/2) = 1sin[(1/2)x + 0) + 0
Period of sin(x/2) = 2π/(1/2) = 4π