f.2數 超急! 唔該 !(20)

1.
(sinθ + cosθ)/(sinθ - cosθ) + (sinθ - cosθ)/(sinθ + cosθ)

= [(sinθ + cosθ)2 + (sinθ - cosθ)2]/(sinθ - cosθ)(sinθ + cosθ)

= (sin2θ + 2sinθcosθ + cos2θ + sin2θ - 2sinθcosθ + cos2θ)/(sinθ - cosθ)(sinθ + cosθ)

= 2(sin2θ + cos2θ)/(sinθ - cosθ)(sinθ + cosθ)

= 2/(sinθ - cosθ)(sinθ + cosθ)

（若是中二，計算到此為止。若是中四，還要繼續計下。）

（中四的答案是 -2/cos2θ）



2.
Assume that 0o ≤ θ ≤ 360o

2cos(θ - 20o) = 1

cos(θ - 20o) = 1/2

(θ - 20o) = 60o OR (θ - 20o) = 360o - 60o

θ = 80o OR θ = 320o

（若只計算 0 至 90o，則答案只有θ = 80o）


3.
2/a : 3/b : 4/c = 1 : 2 : 3

(2/a) = k, (3/b) = 2k and (4/c) = 3k

Then a = 2/k, b = 3/2k and c = 4/3k

a : b : c = 2/k : 3/2k : 4/3k

Hence, a : b : c = 12 : 9 : 8
=