Question

Which of the following would be an acceptable first step in simplifying the expression (sinx)/(1 + sinx) ?. A.1/(cscx + sinx). B.sinx + 1. C.(sinx(1 - sinx))/((1 + sinx)(1 - sinx))

Answer 1

Answer:

$\frac{sinx(1-sinx)}{(1+sinx)(1-sinx)}$

Step-by-step explanation:

$\frac{sinx}{1+sinx}$

To simplify the denominator part we multiply 1+sinx by its conjugate

The conjugate of 1+ sinx  is 1-sinx

Multiply both top and bottom by 1-sinx

$\frac{sinx(1-sinx)}{(1+sinx)(1-sinx)}$

So the acceptable first step in simplifying the expression is multiply by its conjugate at the top and bottom

Answer 2

We are given with the function (sinx)/(1 + sinx). To simplify the equation, we multiply the denominator with its conjugate. Hence the expression becomes (sinx)(1-sin x )/(1 + sinx)(1-sin x). Then we convert the expression into (sinx)(1-sin x )/ cos^2 x. Using trigonometric functions, we can then simplify the expression.