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

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是 [ 1 -(tan x)^2 ] / [ 1 +(tan x)^2 ] = (cos x)^2 -(sin x)^2 吗？猜如
= = = = = = = = =

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.

= = = = = = = = =
分子分母段汪同时乘以 (cos x)^2 ，传说握兆仔中的切割化弦。

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由万能公式察哪，得cos4x=(1-tan²2x)/(1+tan²2x).
由2倍角蔽运公式，得cos²2x-sin²宏没梁2x=cos4x.
左边右边都等于cos4x.
请采纳！

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

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