a math urgent !!

2007-05-04 5:18 am
hkcee 1991
Qs 18
a) Given that tanx = ktany
i ) Show that sin(x+y)=(k+1)cosxsiny.
ii)Hence, show that (k+1)sin(x-y)=(k-1)sin(x+y).
更新1:

also bii) and c, thz~ b) Given that tan(Θ+10°)= ktan(Θ-20°) has solution in Θ. i) Show that sin(2Θ-10°)= (k+1)/2(k-1). ii) Hence, find the range of possible values of k. c) Find the general solution of tan(Θ+10°)= -2tan(Θ-20°), correct the answer to nearest 0.1 degree.

回答 (1)

2007-05-04 5:33 am
✔ 最佳答案
ai tan X = K tan Y
sinx / cosx = k siny/cosy
sinxcosy = k siny cosx -----(1)

SO, sin(x+y) = sinx cosy + siny cosx
= ksiny cos X + siny cosx BY(1)
= (k+1) siny cosx
= (k+1) cosx siny

ii since sin(X+Y)= (K+1) COSX SINY
so sin(x - Y) = (K-1) cosX sinY ----- (2)

(2) sin(x - Y) = (K-1) cosX sinY
(k+1)sin(x - Y) = (k+1)(K-1) cosX sinY
= (k-1) [(k+1) cosX sinY]
= (k-1) sin(X+y)


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