Question

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

Answer 1

Explanation:

The expression is given below as

$\frac{sinx}{1-cosx}$

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

$\begin{gathered} \frac{s\imaginaryI nx}{1-cosx}\times\frac{1+cosx}{1+cosx} \\ =\frac{sinx(1+cosx)}{(1-cosx)(1+cosx)} \end{gathered}$

Hence,

The final answer is

$\frac{s\imaginaryI nx(1+cosx)}{(1-cosx)(1+cosx)}$

OPTION D is the correct answer