Question

Evaluate $\tan (\mathrm{x}+\frac{\mathrm{\pi }}{4})$

Answer 1

To evaluate: $\tan (\mathrm{x}+\frac{\mathrm{\pi }}{4})$

We know that the radian value of $\mathrm{\pi }={180}^0$

So, $\frac{\mathrm{\pi }}{4}=\frac{{180}^0}{4}$$={45}^0$

⇒ $\tan \frac{\mathrm{\pi }}{4}$ $=\tan {45}^0$$=1$

We know that $\tan (\mathrm{A}+\mathrm{B})=\frac{\mathrm{tanA}+\mathrm{tanB}}{1-\mathrm{tanAtanB}}$

⇒ $\tan (\mathrm{x}+\frac{\mathrm{\pi }}{4})$$=\frac{\mathrm{tanx}+\tan {\displaystyle \frac{\mathrm{\pi }}{4}}}{1-\mathrm{tanxtan}\frac{\mathrm{\pi }}{4}}$

$=$$\frac{\mathrm{tanx}+\tan {45}^0}{1-\mathrm{tanxtan}{45}^0}$

$=$$\frac{\mathrm{tanx}+1}{1-\mathrm{tanx}\times 1}$

$=$$\frac{1+\mathrm{tanx}}{1-\mathrm{tanx}}$

Thus, the required value of $\tan (\mathrm{x}+\frac{\mathrm{\pi }}{4})$$=$$\frac{1+\mathrm{tanx}}{1-\mathrm{tanx}}$