Question

（1减去sinx）除于cosx为什么等于tan2分之x

Answer 1

错了。
(1 -sinx)/cosx = [ 1 -tan (x/2) ] / [ 1 +tan (x/2) ].
应该是：
(1 -cos x) /sin x = tan (x/2),
或：
sin x /(1 +cos x) = tan (x/2).

= = = = = = = = =

1. (1 -cos x) /sin x = tan (x/2).
证明：因为 cos x =1 -2 [ sin (x/2) ]^2,
sin x = 2 sin (x/2) cos (x/2),
所以 (1 -cos x) /sin x = 2 [ sin (x/2) ]^2 / [ 2 sin (x/2) cos (x/2) ]
= sin (x/2) / [ cos (x/2) ]
= tan (x/2).

= = = = = = = = =

2. sin x /(1 +cos x) = tan (x/2).
证明：因为 sin x = 2 sin (x/2) cos (x/2),
cos x = 2 [ cos (x/2) ]^2 -1,
所以 sin x /(1 +cos x) = ... =tan (x/2).

= = = = = = = = =
同理,
(1 +cos x) /sin x =sin x /(1 -cos x) = cot (x/2).

cos x = [ cos (x/2) ]^2 -[ sin (x/2) ]^2
= 1 -2 [ sin (x/2) ]^2
= 2 [ cos (x/2) ]^2 -1,
公式的选取很关键.

Answer 2

(1-y/r)/(x/r)=1/(x/r)-(y/r)/(x/r)=r/x-y/x=(r-y)/x=tan(x/2)