Cosine and Tangent

1. Jun 17, 2011

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

2. Jun 17, 2011

lavinia

what have you tried?

3. Jun 17, 2011

MatheusMkalo

I need a demonstration of how to get this formula

4. Jun 17, 2011

HallsofIvy

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

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

5. Jun 17, 2011

MatheusMkalo

I tried to find, but fail =/

6. Jun 17, 2011

micromass

Staff Emeritus
What is the definition of the tangent?

7. Jun 17, 2011

MatheusMkalo

no... the demonstration of the formula..

8. Jun 17, 2011

micromass

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

9. Jun 17, 2011

MatheusMkalo

x? lol '-'

10. Jun 17, 2011

micromass

Staff Emeritus
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. Jun 17, 2011

MatheusMkalo

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

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

12. Jun 17, 2011

micromass

Staff Emeritus
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. Jun 17, 2011

MatheusMkalo

cos²(x)+sin²(x) = 1

That?

14. Jun 17, 2011

Staff: Mentor

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

15. Jun 17, 2011

tiny-tim

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