Question

Which of the following would be an acceptable first step in simplifying the expression sinx/1-cosx

Answer 1

Step-by-step explanation:

The expression is given below as

`(sinx)/(1-cosx)`

Hence,from the expression above,

`\begin{gathered} denominator=1-cosx \\ numerator=sinx \\ sinx,cant\text{ be simplified} \\ 1-cosx,cant\text{ be simplified further} \end{gathered}`

Hence,

The first step is for us to rationalize the denominator by multiplying both the numerator and denominator by its conjugate

The conjugate is given below as

`1+cosx`

By rationalizing the denominator, we will have

`\begin{gathered} (s\imaginaryI nx)/(1-cosx)*(1+cosx)/(1+cosx) \\ =(sinx(1+cosx))/((1-cosx)(1+cosx)) \end{gathered}`

Hence,

The final answer is

`(s\imaginaryI nx(1+cosx))/((1-cosx)(1+cosx))`

OPTION D is the correct answer