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you knew how to solve these simultaneous equations.
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But I want you to realize that
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the solving of the simultaneous equations for T1 and T2
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involve forming combinations of these coefficients
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to eliminate either T1 or T2.
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So, when you add them, one of them drops out.
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And that doesn't depend on
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whether these are trigonometric functions
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or any other numbers,
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they're eliminated in the same way.
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Likewise on the right hand side,
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instead of some numbers like 3 and 4,