How do you simplify #sqrt(1+tan^2x)#?
1 Answer
Jan 13, 2017
Explanation:
Using:
#cos^2 x + sin^2 x = 1#
#tan x = sin x / cos x#
#sec x = 1/cos x#
we find:
#sqrt(1+tan^2 x) = sqrt(1+(sin^2 x)/(cos^2 x))#
#color(white)(sqrt(1+tan^2 x)) = sqrt((cos^2 x)/(cos^2 x)+(sin^2 x)/(cos^2 x))#
#color(white)(sqrt(1+tan^2 x)) = sqrt((cos^2 x+sin^2 x)/(cos^2 x))#
#color(white)(sqrt(1+tan^2 x)) = sqrt(1/(cos^2 x))#
#color(white)(sqrt(1+tan^2 x)) = sqrt(sec^2 x)#
#color(white)(sqrt(1+tan^2 x)) = abs(sec x)#