# Homework Help: 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

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

What is the definition of the tangent?

7. Jun 17, 2011

### MatheusMkalo

no... the demonstration of the formula..

8. Jun 17, 2011

### micromass

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

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

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?