Question

If root 3 cot square theta-4cot theta + root 3=0 find the value of cot square theta +tan square theta

Answer 1

the answer of your question is here

Answer 2

Given:

If root 3 cot square theta-4cot theta + root 3=0

To Find:

the value of cot square theta +tan square theta

Solution:

The given equation is $\sqrt{3} cot^2\theta-4cot\theta+\sqrt{3} =0$

Let cot theta be x, now substituting the value as x we get the equation as,

$\sqrt{3} x^2-4x+\sqrt{3} =0$

Now finding the roots of this quadratic equation using the quadratic formula, we have

$x=\frac{4\pm \sqrt{16-12} }{2\sqrt{3} } \\=\sqrt{3} and \frac{1}{\sqrt{3} }$

So now if cot theta is equal to x then,

$cot\theta =\sqrt{3} ,\frac{1}{\sqrt{3} } \\\theta=30^{\circ},60^{\circ}$

Now finding the value of the given equation as the value of cot \theta at 30 and 60 degrees is inverse so the value for the given equation will be the same for 30 and 60 degrees.

Now, put the values, we have

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

Hence, the value of cot square theta +tan square theta is 10/3.