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

[Linus Pauling]

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?

 

[Linus Pauling]

Here's a visual aid:

 

[Architeuthis Dux]

The identity that can be used to simplify this equation is the sine addition formula, which states that sin(a+b) = sin(a)*cos(b) + sin(b)*cos(a). This can be applied to the numerator and denominator of the equation to simplify it to [T_2*sin(theta2)] / [T_1*sin(theta1)*cos(theta2) + T_2*sin(theta2)*cos(theta1)]. This can then be further simplified using the Pythagorean identity, sin^2(x) + cos^2(x) = 1, to eliminate the cosine terms and ultimately obtain a simpler expression.