Question

If theta = 60 then 1+tan2 theta / 2 tan theta is equal to

Answer 1

Answer:

The answer is:

$\dfrac{1-\sqrt 3}{2\sqrt 3}$

Step-by-step explanation:

Hence as the given question is:

$\theta=60\°$

Then, we have to calculate the value of $\dfrac{1+tan2\theta}{2\ tan\theta}$.

Plugging the value of $\theta$ here:

$=\dfrac{1+tan(2\times 60\°)}{2\ tan60\°}\\=\dfrac{1+tan(120\°)}{2\ tan60\°}$

Value of:

$tan(120\°)=tan(180\°-60\°)}\\tan120\°=-tan60\°\\tan120\°=-\sqrt 3$

Hence substituting the value of, $tan(120\°)$ we get:

$=\dfrac{1+-\sqrt 3}{2\sqrt 3}\\=\dfrac{1-\sqrt 3}{2\sqrt 3}$