有幾道F.5數學題不懂怎樣做,高手請進

1. complete the identify
sinθ((sin(4θ)+sin(6θ))=?
answer (c)

a. 1/2cosθ(4(θ)+cos(6θ))
b. cosθ(cos(4θ)+cos(6θ))
c. cosθ(cos(4θ) - cos(6θ))
d. 1/2 cosθ(cos (4θ) - cos(6θ))

Proof:
sinθ((sin(6θ)+sin(4θ))= sinθ(2sin5θcosθ)
sinθ((sin(6θ)+sin(4θ))= 2cosθsin5θsinθ
sinθ((sin(6θ)+sin(4θ))= 2cosθ (-1/2)(cos6θ – cos4θ}
sinθ((sin(6θ)+sin(4θ))= cosθ (-1)(cos6θ – cos4θ}
sinθ((sin(6θ)+sin(4θ))= cosθ (cos4θ - cos6θ}

2. sin( tan^ -1 multiple u/suare root 2)
Check your spelling or typo error. The way I guess is

Sin[ tan^ -1(u/square root 2)]
tan θ = u/2^0.5
opposite side = u, adjacent side = square root of 2, hypotenuse = (u^2 + 2)^0.5
sin θ = u/(u^2 + 2)^0.5

3. r= 5/(1 + cos θ)
answer (b)

a. y^2=10x-25
b. y^2=25-10x

Proof:
r= 5/(1 + cos θ)
r(1 + cos θ) = 5
r + rcos θ = 5
(x^2 + y^2)^0.5 + x = 5
(x^2 + y^2)^0.5 = 5 – x
Square on both sides
x^2 + y^2 = (5 – x)^2
x^2 + y^2 = 25 – 10x + x^2
y^2 = 25 – 10x

4. find the coordinates of the vertex of the parabola
f(x)= (x+2)^2 + 9
a. (9,-2)
B. (-2,9)

answer (b)
The vertex is (-2, 9)