Question

tan 80⁰ +tan 40⁰/1-tan80⁰.tan 40⁰


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Answer 1

Answer:

The answer is $-\sqrt 3$

Step-by-step explanation:

Using the formula

   $\tan(A+B)=\dfrac{\tan A+\tan B}{1-\tan A\tan B}$

Therefore

$\dfrac{\tan 80^\circ+\tan 40^\circ}{1-\tan 80^\circ\tan 40^\circ}=\tan(80^\circ+40^\circ)\\\\=\tan (120^\circ)=\tan(180^\circ-60^\circ)$

Now using $\tan(180^\circ-\theta)=-\tan\theta$

                  $=-\tan 60^\circ=-\sqrt 3$