Given that cos x =p find an expression, in terms of p, for tan^2 x?

2 Answers
Oct 12, 2015

tan^2x= (1-p^2)/p^2

Explanation:

If cos x =p, sinx= sqrt(1-p^2)

tan x = sqrt(1-p^2)/p

tan^2x= (1-p^2)/p^2

Oct 12, 2015

tan^2 x = (1-p^2)/p^2 = 1/p^2 - 1

Explanation:

If cos x = p, then

cos^2 x = p^2.

By Pythagoras, sin^2 x + cos^2 x = 1, so:

sin^2 x = 1 - cos^2 x = 1 - p^2

Now tan x = sin x / cos x, so

tan^2 x = sin^2 x / cos^2 x = (1 - p^2)/p^2 = 1/p^2 - 1