Question

How do I simplify the following expression by writing it as a term with only one trigonometric function?

(4-2sec^2(x))/(sec^2(x))

Answer 1

2 cos (2x)

Explanation:

`(4 -2 sec^2x)/(sec^2x) \\=(4-(2)/(cos^2x) )/((1)/(cos^2 x) ) \\=((4 cos^2x-2)/(cos^2 x) )/((1)/(cos^2x) ) \\=(2(2 cos^2x-1))/(cos^2x) * (cos^2x)/(1) \\=2(2cos^2x-1)\\=2cos(2x)`