+26393 Find \(\tan^2(20) + \tan^2(40) + \tan^2(80) \) . All angles are in degrees.
Formula:
\(\begin{array}{rcll} \boxed{ \sum \limits_{l=1}^{n} \tan^2\left( \dfrac{180^\circ \cdot l}{2n+1} \right) = n(2n+1) } \\ \end{array}\)
\(\begin{array}{|lrcll|} \hline n=1: & \sum \limits_{l=1}^{1} \tan^2\left( \dfrac{180^\circ \cdot l}{2\cdot 1+1} \right) &=& 1\cdot(2\cdot 1 +1) \\ & \sum \limits_{l=1}^{1} \tan^2\left( \dfrac{180^\circ \cdot l}{3} \right) &=& 1\cdot(3) \\ & \mathbf{ \tan^2\left(60^\circ\right)} &=& \mathbf{ 3 } \\ \hline n=4: & \sum \limits_{l=1}^{4} \tan^2\left( \dfrac{180^\circ \cdot l}{2\cdot 4+1} \right) &=& 4\cdot(2\cdot 4 +1) \\ & \sum \limits_{l=1}^{4} \tan^2\left( \dfrac{180^\circ \cdot l}{9} \right) &=& 4\cdot(9) \\ & \mathbf{\tan^2\left(20^\circ\right)+\tan^2\left(40^\circ\right)+\tan^2\left(60^\circ\right)+\tan^2\left(80^\circ\right) } &=& \mathbf{ 36 } \\ \hline & \tan^2\left(20^\circ\right)+\tan^2\left(40^\circ\right)+\tan^2\left(80^\circ\right) &=& 36 - 3 \\ & \mathbf{\tan^2\left(20^\circ\right)+\tan^2\left(40^\circ\right)+\tan^2\left(80^\circ\right)} &=& \mathbf{33} \\ \hline \end{array}\)
+159 Bro just use the web 2.0 caculator
First go to Home located in the top menu
then you should be able to find the calculator in the middle of your screen.
+2863 Yup thats what I did
I just copy pasted into the amazing calculator and it cheated homework for me.
no jk lol.
But seriously some homework questions are actually dumb. I don't know if the government is trying to steal our brain cells or something.
+2863 if i log out, and post, and log back in. It would make that post mine through the magical use of cookies
yes Sherlock Holmes, the tone of my voice sounded as if I was the one asking the question. 
+26393 Find \(\tan^2(20) + \tan^2(40) + \tan^2(80) \) . All angles are in degrees.
Formula:
\(\begin{array}{rcll} \boxed{ \sum \limits_{l=1}^{n} \tan^2\left( \dfrac{180^\circ \cdot l}{2n+1} \right) = n(2n+1) } \\ \end{array}\)
\(\begin{array}{|lrcll|} \hline n=1: & \sum \limits_{l=1}^{1} \tan^2\left( \dfrac{180^\circ \cdot l}{2\cdot 1+1} \right) &=& 1\cdot(2\cdot 1 +1) \\ & \sum \limits_{l=1}^{1} \tan^2\left( \dfrac{180^\circ \cdot l}{3} \right) &=& 1\cdot(3) \\ & \mathbf{ \tan^2\left(60^\circ\right)} &=& \mathbf{ 3 } \\ \hline n=4: & \sum \limits_{l=1}^{4} \tan^2\left( \dfrac{180^\circ \cdot l}{2\cdot 4+1} \right) &=& 4\cdot(2\cdot 4 +1) \\ & \sum \limits_{l=1}^{4} \tan^2\left( \dfrac{180^\circ \cdot l}{9} \right) &=& 4\cdot(9) \\ & \mathbf{\tan^2\left(20^\circ\right)+\tan^2\left(40^\circ\right)+\tan^2\left(60^\circ\right)+\tan^2\left(80^\circ\right) } &=& \mathbf{ 36 } \\ \hline & \tan^2\left(20^\circ\right)+\tan^2\left(40^\circ\right)+\tan^2\left(80^\circ\right) &=& 36 - 3 \\ & \mathbf{\tan^2\left(20^\circ\right)+\tan^2\left(40^\circ\right)+\tan^2\left(80^\circ\right)} &=& \mathbf{33} \\ \hline \end{array}\)
