Question

show that (cos^4theta-sin^4theta)/cos^2theta=1-tan^2theta

Answer 1

(cos[theta]+tan[theta])/(sin[theta])
cos[theta]/sin[theta] + tan[theta]/sin[theta]
cot[theta] + 1/cos[theta]
cot[theta] + sec[theta]

Answer 2

that doesn't prove it

Answer 3

1st factorise the numerator

(\[\frac{(\cos^2\theta + \sin^2\theta)(\cos^2\theta - \sin^2\theta)}{\cos^2\theta}\]

use

\[\cos^2\theta + \sin^2 \theta = 1\]

then the problem is

\[\frac{1\times(\cos^2\theta - \sin^2\theta)}{\cos^2\theta}\]

then splitting the terms in the numerator

\[\frac{\cos^2\theta}{\cos^2 \theta} - \frac{\sin^2\theta}{\cos^2\theta}\]

using

\[\tan \theta =\frac{\sin \theta}{\cos \theta}\]

gives

\[1 - \tan^2 \theta\]