Solve 5x tan (8x ) =3x .
Solution : Firstly, before we even begin solving we have to make one thing clear. DO NOT CANCEL AN x FROM BOTH SIDES!!! Whereas this may appear like a natural thing to do it WILL cause us to lose solution here.
Hence, to solve this equation first we'll get all the terms on one side of the equation & then factor out an x of the equation. If we can cancel out an x from all terms then it can be factored out. Doing this gives,
5x tan (8x ) - 3x = x (5 tan(8x ) - 3) = 0
Upon factoring we can illustrates that we ought to have either,
x= 0 OR tan (8x ) = 3/5
Note as well that if we'd canceled out the x we would have missed the first solution. Now, we solved out an equation along with a tangent in it in previous section hence we'll not go into the details of this solution here. Following is the solution to the trig equation.
x= 0.0676 + ? n/4 n= 0, ±1, ±2,..........
x= 0.4603 + ? n/4
The complete set of solutions then to the original equation is following,
x= 0
x= 0.0676 + ? n/4
x= 0.4603 + ? n/4
n= 0, ±1, ±2,..........