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Proving Trigonometric Identities by Graphical Method
Proving identities
y = cos 2(x) is identical to
y = 1 - 2 sin2 (x)
By using graphical method of proving it is easy to see that the two graphs are identical therefore it proves that cos 2(x) = 1 - 2 sin2 (x)

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)=cos(2x) then press enter button in your keyboard
Step 4: Enter in input as is: g(x)=1-2sin(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.
By Apolinario "Sam" Ortega, 19 January 2013, Created with GeoGebra
| Given function, f(x) = |
Given another function, g(x)= |
|---|---|
| sin(2x) = | 2sin(x)cos(x) |
| sin(x)/cos(x) = | tan(x) |
| cos(2x) = | 1-2sin2(x) |
| cos2(x) + sin2(x) = | 1 |
| (1-cos(2x)) / (1-sin2(x)) = | 2Tan2(x) |
| tan(x)cot(x)-sin2(x) = | cos2(x) |
| cot(2x) = | (cot2(x)-1) / (2cot(x)) |
| cos(x)/(1-sin(x) = | sec(x) + tan(x) |
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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