What is the Value of Tan 45 Degrees ?

Solution :

The value of tan 45 degrees is 1.

Proof :

Let ABC be a triangle, right angled at B, in which $\angle$ A = $\angle$ C = 45 degrees

$\therefore$  BC = AB

Let  AB = BC = a

Then by pythagoras theorem,

$AC^2$ = $AB^2$ + $BC^2$ = $a^2$ + $a^2$ = $2a^2$

$\implies$  AC = $\sqrt{2}a$

In $\Delta$ ABC,  $\angle$ C = 45 degrees

By using trigonometric formulas,

$tan 45^{\circ}$ = $perpendicular\over base$ = $p\over b$

$tan 45^{\circ}$  = side opposite to 45 degrees/side adjacent to 45 degrees = $AB\over BC$ = $a\over a$ = 1

Hence, the value of $tan 45^{\circ}$ = 1