三角函數 快20點

證明sin@+cos@除sin@-cos@ = tan@+1除tan-1


左方和右方各證明一次



L.H.S
= (sin x + cos x) /(sin x - cos x)
= cos x ( sin x/cos x + 1)/cos x ( sin x /cos x - 1)
= (tan x + 1)/(tan x - 1) = R. H. S.

R. H. S.
= (tan x + 1)/( tan x - 1)
= (sin x/cos x + 1)/(sin x/cos x - 1)
= [(sinx + cos x)/cos x]/[(sin x - cos x)/cos x]
= (sinx + cos x)/(sin x - cos x)
= L.H.S.
加油!Eric祝你學業進步

Q:help me plx hkcee 2007 straight line !!!!! it is given that four points A(0,-2) B(1,-3) C(2,0) and D(k,k) form a quadrilateral ABCD.Find the area of this quadrilateral

Ans:1/2[0(-3)+1(0)+2k+k(-2)-1(-2)-2(-3)-k(0)-0(k)]
=4

L.H.S.= sin@+cos@
sin@-cos@
= cos@tan@+cos@
cos@tan@-cos@
= cos@(tan@+1)
cos@(tan@-1)
= tan@+1
tan@-1
R.H.S. = tan@+1
= tan@-1
Therefore L.H.S. = R.H.S.

L.H.S = (sin x + cos x) /(sin x - cos x)
= cos x ( sin x/cos x + 1)/cos x ( sin x /cos x - 1)
= (tan x + 1)/(tan x - 1) = R. H. S.

R. H. S. = (tan x + 1)/( tan x - 1)
= (sin x/cos x + 1)/(sin x/cos x - 1)
= [(sinx + cos x)/cos x]/[(sin x - cos x)/cos x]
= (sinx + cos x)/(sin x - cos x) = L.H.S.