Question
Question: How do you find all solutions for \(5\sqrt{3}\tan x+3=8\sqrt{3}\tan x\)?...
How do you find all solutions for 53tanx+3=83tanx?
Solution
The given equation in the above question is a simple trigonometric equation which can be solved easily using the basic algebraic manipulations. First of all, we need to separate the variable terms on the LHS and the constant term on the RHS. For this, we first have to subtract 83tanx from both the sides of the given equation. After this, we have to divide the obtained equation by the coefficient of tanx so that we will obtain the equation of the form tanx=tanα. The solution to this equation can be written by using the general solution which is given as x=nπ±α, where n is an integer.
Complete step by step solution:
The trigonometric equation given in the above question is
⇒53tanx+3=83tanx
We subtract 83tanx from both the sides of the above equation to get