why : cos^2 x + sin^2 x =1?

這是關係到畢氏定理的

請看:
http://img195.imageshack.us/img195/6743/pythtrigoz.png

2009-05-31 14:17:32 補充：
嗯.以上的,誰也知道

2009-05-31 14:18:43 補充：
問得出尼個題目既就未學half-angle啦.
你想佢更加唔明!?

2009-05-31 19:06:30 補充：
用PYTH證咪ok = =

Let sin x = a / c and cos x = b / c , where c^2 = a^2 + b^2.

Consider
sin^2 x = a^2 / c^2 ; and
cos^2 x = b^2 / c^2 .

Then, we have
sin^2 x + cos^2 x = (a^2 + b^2) / c^2 = c^2 / c^2 = 1.

Therefore, the result follows.

注意邏輯循環！

LHS= cos^2 x + sin^2 x
= 1/2 ( 1 + cos2x ) + 1/2 ( 1- cos2x)
= 1
= RHS

cos^2 θ+sin^2 θ=1

LHS= cos^2 x + sin^2 x
= 1/2 ( 1 + cos2x ) + 1/2 ( 1- cos2x)
= 1
= RHS

所以 cos^2 x + sin^ 2 x congruent to 1

因為e條係恆等式,,
已經證實左,,
無論代咩答案都係,,1