Question

Which of the following would be an acceptable first step in simplifying the expression sin x/ 1-cos x

Answer 1

the question does not present the options, but this does not interfere with the resolution

we have

sin x/ (1-cos x)

we know that

sin²x+cos²x=1-----------> sin²x=1-cos²x

and

difference of squares

(a+b)*(a-b)=a²-b²

so

The idea is to make the difference of squares (1-cos²x)in denominator.so

multiply the expression by (1+cos x)/(1+cos x)

[sin x/ (1-cos x)]*[(1+cos x)/(1+cos x)]=[sin x*(1+cos x)]/[ (1-cos x)/(1+cos x)]

=[sin x*(1+cos x)]/[ (1-cos²x)]

=[sin x*(1+cos x)]/[ sin²x]

=(1+cos x)/sin x

=(1/sin x)+(cos x/sin x)

=csc x+cot x

therefore

the answer is

the first step is multiply the expression by (1+cos x)/(1+cos x)

Answer 2

Answer:

multiply expression by (1+cos x)/(1+cos x)