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

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Homework Help Overview

The discussion revolves around solving the equation 2 \csc x + 3 \sec x = -\sec x \tan x, which involves trigonometric functions. Participants are exploring methods to manipulate the equation for potential solutions.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss converting all terms to a single trigonometric function and question the definitions of sec, csc, and tan. There is an attempt to express the equation in terms of sine and cosine, but some express difficulty in progressing from that point.

Discussion Status

The discussion is active, with participants offering suggestions on how to simplify the equation further. There is a recognition of the need to multiply by a specific trigonometric function to aid in simplification, although no consensus on the next steps has been reached.

Contextual Notes

Participants are clarifying whether the goal is to prove an identity or to find specific values of x that satisfy the equation. This distinction is noted as important for guiding the approach to the problem.

cscott
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Looking for some help for this equation:

[tex]2 \csc x + 3 \sec x = - \sec x \tan x[/tex]
 
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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.

[tex]\frac{2}{\sin x} + \frac{3}{\cos x} = -\frac{1}{\cos x}\cdot\frac{\sin x}{\cos x}[/tex]
 
Last edited:
cscott said:
Looking for some help for this equation:
[tex]2 \csc x + 3 \sec x = - \sec x \tan x[/tex]

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

Sine! Thanks.
 

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