Question

$\frac{1 + \frac{1 }{ \cos(x) } }{ \frac{1}{ \cos(x) } }$
simplify it​

Answer 1

Answer:

1 + cosx

Step-by-step explanation:

As per the information provided in the question, We have :

• $\longmapsto \rm \dfrac{1 + \dfrac{1 }{ \cos(x) } }{ \dfrac{1}{ \cos(x) } }$

We are asked to simplify it.

Using the fraction rule i.e a/b/c = a × c/b, Thus,

$\\\longmapsto \rm \dfrac{1 + \dfrac{1 }{ \cos(x) } }{ \dfrac{1}{ \cos(x) } }$

$\longmapsto \rm 1 + \frac{1}{ \cos(x) } \times \frac{ \cos(x) }{1}$

$\longmapsto \rm \bigg(1 + \frac{1}{ \cos(x) } \bigg) { \cos(x) }$

$\longmapsto \rm (1 + \sec(x) ){ \cos(x) }$

$\longmapsto \rm 1 + \cos(x)$

This can't be further simplified. Hence, It 1 + cos x is the required answer.

Learn more!

• $\begin{gathered}\qquad \sf \: ( I ) \:sin^2\:\theta \:+\:cos^2 \:\:=\:1\:\\\\\end{gathered}$

• $\begin{gathered}\qquad \sf \: ( II ) \:sin^2\:\theta \:=\: 1 \:-\:cos^2 \:\:\:\\\\\end{gathered}$

• $\begin{gathered}\qquad \sf \: ( III ) \:\:cos^2 \:\:=\:1 \:-\:sin^2\:\theta \:\\\\\end{gathered}$

• $\begin{gathered}\qquad \sf \: ( IV ) \:\:\:1 \:+\:cot^2\:\theta \:=\: cosec^2\:\theta \:\\\\\end{gathered}$

• $\begin{gathered}\qquad \sf \: ( V ) \:\:\:cosec^2\:\theta \:-\:cot^2\:\theta \:=\: 1 \:\\\\\end{gathered}$

• $\begin{gathered}\qquad \sf \: ( VI ) \:\:\:cosec^2\:\theta \:=\:cot^2\:\theta \:+\: 1 \:\\\\\end{gathered}$