证明1-tan^2x/1+tan^2x=cos^2x-sin^2x

题目

证明1-tan^2x/1+tan^2x=cos^2x-sin^2x
我们很多公式没教，应该不能用。有其他麻烦的方法吗

答案

是 [ 1 -(tan x)^2 ] / [ 1 +(tan x)^2 ] = (cos x)^2 -(sin x)^2
= = = = = = = = =
证明：[ 1 -(tan x)^2 ] / [ 1 +(tan x)^2 ]
= { [ 1 -(tan x)^2 ] *(cos x)^2 } / { [ 1 +(tan x)^2 ] *(cos x)^2 }
= [ (cos x)^2 -(sin x)^2 ] / [ (cos x)^2 +(sin x)^2 ]
= (cos x)^2 -(sin x)^2.
= = = = = = = = =
分子分母同时乘以 (cos x)^2 ,传说中的切割化弦.