1=(1-sin^2O)(1+tan^2O)

Question

asked Jul 13, 2019 19.3k views

1 Answer

Konstantin Ershov · Answer 1 · 2019-07-20T14:25:16+0000

I believe the equation is

$1=(1-\sin^2\theta)(1+\tan^2\theta)$

which is true for all
$\theta$ , so I guess you're supposed to show why (i.e. establish the identity). Recall that

$\cos^2\theta+\sin^2\theta=1$

from which we can derive

$\cos^2\theta=1-\sin^2\theta$

$1+\tan^2\theta=\sec^2\theta$

So the original equation is equivalent to

$1=\cos^2\theta\sec^2\theta$

and since
$\sec\theta=\frac1{\cos\theta}$ , the right side reduces to 1.