Discover the Cosine and Tangent Demonstration for cos(x)² = 1/1+tan(x)²

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The discussion focuses on the demonstration of the trigonometric identity cos²(x) = 1/(1 + tan²(x)). Participants emphasize the importance of understanding the definitions of tangent and sine, with one suggesting to substitute tan(x) = sin(x)/cos(x) into the equation. Simplifying the right-hand side leads to the identity cos²(x) + sin²(x) = 1, which is fundamental in trigonometry. The conversation highlights the need for foundational knowledge in trigonometric functions to grasp the demonstration effectively. Ultimately, the participants aim to collaboratively derive the formula through simplification and understanding of trigonometric identities.
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Demontration of:
cos(x)² =
1
\overline{1+tan(x)²}

Anyone know?

If you don't understand:

cos(x)² = 1/1+tan(x)²
 
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MatheusMkalo said:
Demontration of:
cos(x)² =
1
\overline{1+tan(x)²}

Anyone know?

If you don't understand:

cos(x)² = 1/1+tan(x)²

what have you tried?
 
I need a demonstration of how to get this formula
 
Why? Wouldn't it be better to find such a demonstration yourself?

As a hint, look at a standard identity involving tan^2(x).
 
I tried to find, but fail =/
 
MatheusMkalo said:
I tried to find, but fail =/

What is the definition of the tangent?
 
no... the demonstration of the formula..
 
MatheusMkalo said:
no... the demonstration of the formula..

I'm trying to find the demonstration together with you! What is the tangent?
 
x? lol '-'
 
  • #10
MatheusMkalo said:
x? lol '-'

Wait, so you ask us how to prove this formula, and you don't even know what a tangent is? I suggest looking up the definitions and the formulas and then come back.
 
  • #11
I don't understand your question sorry '-'...

tan(x) = sin(x)/cos(x)..
 
  • #12
Yes, tan(x)=sin(x)/cos(x).

Now plug that in into the equation

\cos^2(x)=\frac{1}{1+\tan^2(x)}

and simplify the right-hand side.
 
  • #13
cos²(x)+sin²(x) = 1

That?
 
  • #14
Start with 1/(1 + tan2(x)), and replace the tangent term. Simplify the result.
 
  • #15
MatheusMkalo said:
cos²(x)+sin²(x) = 1

ok, so how can you get from that back to the original equation? :smile:
 
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