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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