How do you simplify #sqrt(1+tan^2x)#?

1 Answer
George C.
Jan 13, 2017

#sqrt(1+tan^2 x) = abs(sec x)#

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)#

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