Hi guys been struggling to solve this
If you know how to do it, please do solve and show work so that I can follow your steps
prove (sec(x)-cos(x))/(sec(x)+cos(x))=(sin^2(x))/(1+cos^2(x))
when proving identities, beginners are advised to change all trig functions to terms involving cosine and/or sine ...
$\displaystyle \frac{\sec{x} - \cos{x}}{\sec{x}+\cos{x}} =$
change $\displaystyle \sec{x}$ to $\displaystyle \frac{1}{\cos{x}}$ ...
$\displaystyle \frac{\frac{1}{\cos{x}} - \cos{x}}{\frac{1}{\cos{x}} + \cos{x}} =$
common denominator ...
$\displaystyle \frac{\frac{1}{\cos{x}} - \frac{\cos^2{x}}{\cos{x}}}{\frac{1}{\cos{x}} + \frac{\cos^2{x}}{\cos{x}}} =$
$\displaystyle \frac{\frac{1 - \cos^2{x}}{\cos{x}}}{\frac{1+\cos^2{x}}{\cos{x}}} =$
use the Pythagorean identity in the numerator ...
$\displaystyle \frac{\frac{\sin^2{x}}{\cos{x}}}{\frac{1+\cos^2{x} }{\cos{x}}} =$
divide the fractions ...
$\displaystyle \frac{\sin^2{x}}{1+\cos^2{x}}$