# Trig Equation

Looking for some help for this equation:

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

HallsofIvy
Homework Helper
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?

HallsofIvy said:
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?

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

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

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hotvette
Homework Helper
cscott said:
Looking for some help for this equation:
$$2 \csc x + 3 \sec x = - \sec x \tan x$$

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?

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hotvette said:
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?

Solve for x.

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

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

Sine! Thanks.