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)