Question

If root 3 cot square theta minus 4 cot theta + root 3 is zero find the value of cot squared theta + tan squared theta

Answer 1

Answer:

$cot^2\theta+tan^2\theta=\frac{10}{3}$

Step-by-step explanation:

$\sqrt{3}cot^2\theta-4\:cot\theta+\sqrt{3}=0\\\\\sqrt{3}cot^2\theta-3\:cot\theta-cot\theta+\sqrt{3}=0\\\\\sqrt{3}cot\theta[cot\theta-\sqrt{3}]-[cot\theta-\sqrt{3}]=0\\\\(\sqrt{3}cot\theta-1)(cot\theta-\sqrt{3})=0\\\\cot\theta=\frac{1}{\sqrt3}\;or\;cot\theta=\sqrt{3}$

when

$cot\theta=\frac{1}{\sqrt3}\\\\cot^2\theta+tan^2\theta\\\\=\frac{1}{3}+3\\\\=\frac{10}{3}$

when

$cot\theta=\sqrt3\\\\cot^2\theta+tan^2\theta\\\\=3+\frac{1}{3}\\\\=\frac{10}{3}$

Answer 2

Answer:

10/3 is the answer.

Step by Step Explanation is done already, upper of mine.