- #1
cscott
- 782
- 1
Looking for some help for this equation:
[tex]2 \csc x + 3 \sec x = - \sec x \tan x[/tex]
[tex]2 \csc x + 3 \sec x = - \sec x \tan x[/tex]
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?
cscott said:Looking for some help for this equation:
[tex]2 \csc x + 3 \sec x = - \sec x \tan x[/tex]
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?
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]?
The equation that needs to be solved is 2\csc x + 3\sec x = -\sec x \tan x.
The first step in solving this equation is to simplify the left side of the equation by using the trigonometric identities for csc x and sec x.
Yes, this equation can be solved algebraically by manipulating the equation using the trigonometric identities and solving for x.
Yes, the solutions for this equation are only valid for certain values of x. The domain is all real numbers except for the values where csc x, sec x, or tan x are undefined.
Yes, there are other methods to solve this equation such as graphing or using a calculator to find the approximate solutions. However, algebraic manipulation is the most common method used.