Question

Can someone please explain this problem step by step? Thank you sooooooooooooo much!

Answer 1

Step-by-step explanation:

Use the Pythagorean identity, cancel common factors, and divide numerator and denominator by cos(x). Equivalently, multiply numerator and denominator by sec(x).

`\frac{\sin^2{x}+2cos(x)-1}{\sin^2{x}+3cos(x)-3}=\frac{1-\cos^2{x}+2cos(x)-1}{1-\cos^2{x}+3cos(x)-3} \qquad\text{replace $\sin^2$ with $1-\cos^2$}\\\\=(cos(x)(2-cos(x)))/((cos(x)-1)(2-cos(x)))=(cos(x))/(cos(x)-1)=(1)/((cos(x))/(cos(x))-(1)/(cos(x)))=\frac{1}{1-\sec{x}}`