A Trigonometrical Ratios

I have a mathematical term of the form tan(A.x)/tan(B.x)=C.How do I find out the value of x?
 

fresh_42

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I would try the addition theorem for sine, since you have ##\sin(Ax) \cos(Bx) = C \sin(Bx) \cos(Cx)##. Or solve it numerically, e.g. by the help of WolframAlpha.com.
 
I would try the addition theorem for sine, since you have ##\sin(Ax) \cos(Bx) = C \sin(Bx) \cos(Cx)##. Or solve it numerically, e.g. by the help of WolframAlpha.com.
By using Addition Theorem,I finally get sin(A+B)x=-sin(A-B)x..Now how do I find x?
 

fresh_42

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By using Addition Theorem,I finally get sin(A+B)x=-sin(A-B)x..Now how do I find x?
I wonder where the ##C## has gone. But if you have what you say, then we can use ##-\sin(\alpha)=\sin(-\alpha)## and then you can apply ##\arcsin##.
 

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