How do I simply this (there should be a trig. identity involved

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The discussion focuses on simplifying a center of mass equation involving tension components and angles. The equation presented is [T_2*sin(theta2)] / [T_1*sin(theta1) + T_2*sin(theta2)]. Participants are seeking a trigonometric identity that can help simplify this expression effectively. Visual aids are provided to assist in understanding the problem. The goal is to identify the appropriate trigonometric identity for simplification.
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1. This was actually a center of mass problem, so I got the equation below:



2.[T_2*sin(theta2)] / [T_1*sin(theta1) + T_2*sin(theta2)]



3. This is part of a solution I obtained for a physics problem. I know there is some trick with a trig indentity that I can use to simplify this. What is the identity?
 
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Here's a visual aid:

MTS_st_24.jpg
 
I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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