# Trig Equation

1. Oct 24, 2005

### cscott

Looking for some help for this equation:

$$2 \csc x + 3 \sec x = - \sec x \tan x$$

2. Oct 24, 2005

### HallsofIvy

Staff Emeritus
Generally, for a problem like this, the best thing to do is change them all to one function. Do you know how sec x, csc x and tan x are defined?

3. Oct 30, 2005

### cscott

I do. I can put it all in sine/cosine but I can't get anywhere from there.

$$\frac{2}{\sin x} + \frac{3}{\cos x} = -\frac{1}{\cos x}\cdot\frac{\sin x}{\cos x}$$

Last edited: Oct 30, 2005
4. Oct 30, 2005

### hotvette

So, what's the question? Is this an identity that you are trying to prove, or are you trying to solve for x that satisfies the equation?

Last edited: Oct 30, 2005
5. Oct 30, 2005

### cscott

Solve for x.

6. Oct 30, 2005

### hotvette

HallsofIvy had the right idea. You just need to go further. Which trig function could you multiply by to simplify the equation $\frac{2}{\sin x} + \frac{3}{\cos x} = -\frac{1}{\cos x}\cdot\frac{\sin x}{\cos x}$?

Last edited: Oct 30, 2005
7. Oct 30, 2005

### cscott

Sine! Thanks.

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