Solve for x using trigonometric ratios

[Sourav Guha]

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]

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.

 

[Sourav Guha]

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]

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 $\arcsin$.