Question

Find the value of $\tan {45}^0$.

Answer 1

Solve for the value of $\tan {45}^0$.

As we know that $\tan \left(x\right)=\frac{\sin \left(x\right)}{\cos \left(x\right)}$

$$\begin{gathered} \tan \left(45°\right)=\frac{\sin (45°)}{\cos (45°)} \\ \Rightarrow \tan \left(45°\right)=\frac{{\displaystyle \frac{1}{\sqrt{2}}}}{{\displaystyle \frac{1}{\sqrt{2}}}}\left[\sin (45°)=\frac{1}{\sqrt{2}},\cos (45°)=\frac{1}{\sqrt{2}}\right] \\ \Rightarrow \tan \left(45°\right)=1 \end{gathered}$$

Hence, the value of $\tan 45°=1$.