Question

Find the value of $\tan {40}^0$.

Answer 1

Expand the value of $\tan 40°$ in standard angles.

$\tan 40°=\tan \left(30°+10°\right)$

$\begin{array}{rcl}\tan 30°& =& \frac{1}{\sqrt{3}},\tan 0°=0,\tan 45°=1,\tan 60°=\sqrt{3}\mathrm{and}\tan 90°=\infty \end{array}$

So, $\tan 40°=\tan \left(30°+10°\right)$. ; $\left[\tan \left(A+B\right)=\frac{\tan A+\tan B}{1-\mathrm{tanAtanB}}\right]$

$\begin{array}{rcl}\tan 40°& =& \frac{\tan 30°+\tan 10°}{1-\tan 30°\tan 10°}\\ & =& \frac{\left(0.57735\right)+\left(0.176326\right)}{1-\left(0.57735\right)\left(0.176326\right)}\\ & =& 0.839095\end{array}$

Hence, the value of $\tan 40°\mathrm{is}0.839095$.