cos^2x+tan^2xcos^2x=1?

0 ⤊

cos^2x+tan^2xcos^2x=1?

2007-10-10 09:04:23 · 2 answers · asked by Jasmine R 2 in Science & Mathematics ➔ Mathematics

2 answers

tan^2x = sin^2 x / cos^2 x

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

cos^2 x + sin^2 x = 1

Proved.
__________________

Factor out cos^2 x

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

1 + tan^2 x = sec^2 x

sec^2 x = 1 / (cos^2 x)

cos^2 x / cos^2 x = 1

Proved again.

2007-10-10 09:07:41 · answer #1 · answered by UnknownD 6 · 0⤊ 0⤋

cos^2x+tan^2xcos^2x=1
tan^2xcos^2x = 1-cos^2x = sin^2x
tan^2x = sin^2x/cos^2x = tan^2x
Thus we have an identity which means x can be anything.

2007-10-10 09:11:44 · answer #2 · answered by ironduke8159 7 · 0⤊ 0⤋