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2(tan x)^2 = (1-cos2(x))/(1-sin(x)^2)
Trigonometric Identities

Proving Trigonometric Identities by Graphical Method

y = 2(tan x)^2 is identical to
y = (1-cos (2x)) / (1-(sin x)^2)

By using graphical method of proving trigonometric identities. It is easy to see that the two functions are identical therefore it proves that
2(tan x)^2 = 1-cos (2x) / (1-(sin x)^2)

Using Google search, you can prove trigonometric identity using graphical method. just by searching the function separated by comma symbol ,

INSTRUCTION ON HOW TO USE GEOGEBRA:

Step 1: Delete text1 by selecting it and then selecting ⊠
Step 2: Delete conic equation labeled "c" and "d" and then selecting ⊠
Step 3: Enter in input as is: f(x)=2(tan x)^2 then press enter button in your keyboard
Step 4: Enter in input as is: j(x)= (1-cos (2x))/ (1-(sin x)^2) press enter button in your keyboard

You will notice that the two graphs are identical therefore it proves that the two trigonometric function are identical meaning you can use either one of the functions and the answer will be identical.

Apolinario "Sam" Ortega, 19 January 2013, Created with Geogebra

Cos (2x) Identity Sine (2x) Identity Tan x Identity Cos ² (x) + Sin ² (x) Identity

2 Tan ² (x) Identity Cos ² (x) Identity Cot 2x Identity

Cos x / (1-Sin x) Identity

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