Question

Why is \[\tan (0) = 0\]?

Answer 1

Hint: The given question is related with trigonometry, and is to prove that the value of “tan” at zero degree is zero, here we need to prove it by making a triangle in which the angle between perpendicular and base of triangle would be zero.
Formulae Used: The trigonometric identity “tan” is expressed as:
\[ \Rightarrow \tan \theta = \dfrac{{perpendicular}}{{base}}\]

Complete step-by-step solution:
Here to solve the above question we know that the ratio of the perpendicular length to the base length of the right angle triangle is expressed as “tan” identity, to solve this let’s assume a right angle triangle, on drawing we get:

Here the ratio of side AB and BC will give the value for “tan”, and to make the angle theta we have to touch AC with the side BC hence the side AB will diminish, hence the ratio will become as:
\[ \Rightarrow \tan (0) = \dfrac{0}{{BC}} = 0\](as length AB is now diminished to zero)
Hence, proved the above asked identity in the question.

Note: The trigonometric angles are defined by the help of triangles, and to show or proof the angels we have to use the right angle triangle. Here as identity “tan” was asked so angle theta was considered accordingly, if any other identity would be asked then we have to solve it accordingly.