Question

How do you solve $\tan x = 1?$

Answer 1

Hint: In the given question, we have been asked the value/ values of x when $\tan x$ becomes $1 $. For solving such questions there are many ways but we will find the value of x by a very simple method.
First we will use trigonometry’s basic formula $\tan x = \dfrac{{\sin x}}{{\cos x}}$. As you know now the value of x when $\tan x$ becomes $1$ and value of x when $\sin x = \cos x$ is the same.

Formula used:
For finding the value/ values of x when $\tan x$ become $1$ we will use below given formulas:
$
   \Rightarrow \tan x = \dfrac{{\sin x}}{{\cos x}} \\
   \Rightarrow \sin {45^ \circ } = \dfrac{1}{{\sqrt 2 }} \\
   \Rightarrow \cos {45^ \circ } = \dfrac{1}{{\sqrt 2 }} \\
$

Complete step by step answer:
For finding the value/ values of x when $\tan x$ become $1$ we are going to use this formula:
$\tan x = \dfrac{{\sin x}}{{\cos x}}$
Now, in this question $\tan x = 1$. So ,
$ \Rightarrow \tan x = \dfrac{{\sin x}}{{\cos x}} = 1$
Or
$ \Rightarrow \sin x = \cos x$
Now we know that values of sin and cos will became same when $x = \dfrac{\pi }{4} = {45^ \circ }$

So, $\tan x = 1$when $x = \dfrac{\pi }{4} = {45^ \circ }$

Note:
So as you know now for solving such types of questions you have to understand the given question. Do not memorize solutions. After understanding the question, think of the best way to solve it and after that write what you need for solving the question. Then write a step by step answer.