Answer of given expression is [tex]{cos2(x)} =cos^{2} (x)-sin^{2} (x)[/tex]
What is Trigonometric functions?
Trigonometric functions defined as the functions which show the relationship between angle and sides of a right-angled triangle.
Given,
[tex]\frac{cos2(x)}{cos(x)-sin(x)}[/tex]
where [tex]{cos2(x)} =cos^{2} (x)-sin^{2} (x)[/tex]
so, [tex]\frac{cos^{2} (x)-sin^{2} (x)}{cos(x)-sin(x)}[/tex]
[tex]\frac{(cos(x)-sin(x))(cos(x)+sin(x))}{cos(x)-sin(x)}[/tex]
[tex]cos(x)+sin(x)[/tex]
Learn more about Trigonometric functions
https://brainly.com/question/6904750
#SPJ2
