Proving cos(x)² = 1/(1+tan(x)²)

[MatheusMkalo]

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

 

[lavinia]

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?

 

[MatheusMkalo]

I need a demonstration of how to get this formula

 

[HallsofIvy]

Why? Wouldn't it be better to find such a demonstration yourself?

As a hint, look at a standard identity involving $tan^2(x)$.

 

[MatheusMkalo]

I tried to find, but fail =/

 

[micromass]

I tried to find, but fail =/

What is the definition of the tangent?

 

[MatheusMkalo]

no... the demonstration of the formula..

 

[micromass]

no... the demonstration of the formula..

I'm trying to find the demonstration together with you! What is the tangent?

 

[MatheusMkalo]

x? lol '-'

 

[micromass]

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.

 

[MatheusMkalo]

I don't understand your question sorry '-'...

tan(x) = sin(x)/cos(x)..

 

[micromass]

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.

 

[MatheusMkalo]

cos²(x)+sin²(x) = 1

That?

 

[Mark44]

Start with 1/(1 + tan²(x)), and replace the tangent term. Simplify the result.

 

[tiny-tim]

cos²(x)+sin²(x) = 1

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