Final answer:
To solve the equation tan²x - tanx - √3tanx = √3, substitute tanx with a variable, u, then solve the quadratic equation using the quadratic formula and find x using the inverse tangent.
Step-by-step explanation:
To solve the equation tan²x - tanx - √3tanx = √3, we can substitute tanx with a variable, let's say u. This will transform the equation into a quadratic equation in terms of u. So we have u² - u - √3u = √3. Simplifying the equation, we get u² - (1 + √3)u + √3 = 0. Using the quadratic formula, we can solve for u and then solve for x by taking the inverse tangent of u.