Question

Evaluate: $\tan \frac{\mathrm{\pi }}{4}$

Answer 1

To evaluate $\tan \frac{\mathrm{\pi }}{4}$

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$

We know the identity $\mathrm{tanA}=\frac{\mathrm{sinA}}{\mathrm{cosA}}$, we get

So, $\tan \frac{\mathrm{\pi }}{4}$ $=$$\frac{\sin {45}^0}{\cos {45}^0}$

$=$$\frac{\frac{1}{\surd 2}}{\frac{1}{\surd 2}}$ (From trigonometric table $\sin {45}^0=\frac{1}{\surd 2}$and $\cos {45}^0=\frac{1}{\surd 2}$)

$=\frac{1}{\surd 2}\times \frac{\surd 2}{1}$

$=1$

Thus, the required value of $\tan \frac{\mathrm{\pi }}{4}$$=1$