Question

If root 3sinA-cosA =0,prove that... ​

Answer 1

$\begin{aligned}\text{LHS}\implies\ \ &\tan(3\theta)\\\\\implies\ \ &\tan(2\theta+\theta)\\\\\implies\ \ &\dfrac{\tan(2\theta)+\tan\theta}{1-\tan(2\theta)\tan\theta}\\\\\implies\ \ &\dfrac{\frac{2\tan\theta}{1-\tan^2\theta}+\tan\theta}{1-\frac{2\tan^2\theta}{1-\tan^2\theta}}\\\\\implies\ \ &\dfrac{3\tan\theta-\tan^3\theta}{1-3\tan^2\theta}\ \ \implies\ \ \text{RHS}\end{aligned}$

This proof holds true for every values of  $\theta,$  not only for those values which satisfy the equation  $\sqrt3\sin\theta-\cos\theta=0.$

Hence the equation is given just for confusing in my opinion!