What is cos^2x if tanx=4?

We'll start from the fundamental formula of
trigonometry:

(sin x)^2 + (cos x)^2 =
1

We'll divide by (cos x)^2 both
sides:

(sin x)^2/ (cos x)^2 + 1 = 1/(cos
x)^2

But the ratio (sin x)^2/ (cos x)^2 = (tan
x)^2

(tan x)^2 + 1 = 1/(cos
x)^2

From enunciation, we know that tan x =
4.

We'll square raise both
sides:

(tan x)^2 = 16

16 + 1 =
1/(cos x)^2

1/(cos x)^2 =
17

(cos x)^2 =
1/17