Solving the 2\csc x + 3\sec x = -\sec x \tan x Equation

[cscott]

Looking for some help for this equation:

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

 

[HallsofIvy]

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?

 

[cscott]

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}

 

[hotvette]

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?

 

[cscott]

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]

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}?

 

[cscott]

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.