Trigonometric Equations - Trouble solving

[Eliotmason]

\(\displaystyle 3\csc^{2}\frac{x}{2}=2\sec x\)

First off this is not proving identities. It is solving equations to find the angles associated with the above equation.

So I have been on this question for a while now and can't seem to get anywhere. I think I am having the most trouble trying to perform the reciprocal on the equation so I can see easier terms like sin and cos.


1. If I perform the reciprocal on this equation does it become this:

\(\displaystyle \frac{1}{3}\sin^{2}\frac{x}{2}=\frac{1}{2}\cos x\)

-or do I also have to do something with the x/2?


-so confused. Thank you for your help ahead of time

 

[Romsek]

\(\displaystyle 3\csc^{2}\frac{x}{2}=2\sec x\)

First off this is not proving identities. It is solving equations to find the angles associated with the above equation.

So I have been on this question for a while now and can't seem to get anywhere. I think I am having the most trouble trying to perform the reciprocal on the equation so I can see easier terms like sin and cos.


1. If I perform the reciprocal on this equation does it become this:

\(\displaystyle \frac{1}{3}\sin^{2}\frac{x}{2}=\frac{1}{2}\cos x\)

-or do I also have to do something with the x/2?


-so confused. Thank you for your help ahead of time

you're on the right track so far.

next what I would do is convert sin²(x/2) into an expression involving cos²(x/2), and then use the half angle formula to express that in terms of x.

Slog through the algebra and you should have it.

 

[Eliotmason]

Got it! thank you for your help