# Math Help - Simplify trig equation

1. ## Simplify trig equation

How do I simply $(1+tan^2A)(1-sin^2A)$

2. Hello,
Originally Posted by zapparage
How do I simply $(1+tan^2A)(1-sin^2A)$
You can start by using $1+\tan^2A=\frac{1}{\cos^2A}$. If you're not supposed to know this identity you can start as follows :

$
(1+\tan^2A)(1-\sin^2A)=(1+\tan^2A)\cos^2A=\left(1+\frac{\sin^2A} {\cos^2A}\right)\cos^2A=\ldots$

3. It Equals 1, it may take me a lil while to post the answer since I'm trying to learn latex lol.

4. ${1-sin^2A} = cos^2A$

5. Here is another way you could do it,

$1- sin^2A +tan^2A-tan^2Asin^2A= 1 -sin^2A +\frac{sin^2A}{cos^2A} -\frac{sin^4A}{cos^2A}$

$\frac{cos^2A-sin^2Acos^2A+sin^2A-sin^4A}{cos^2A}$

$\frac{cos^2A(1-sin^2A)+sin^2A(1-sin^2A)}{cos^2A}$

$\frac{cos^4A+sin^2Acos^2A}{cos^2A}$

$\frac {cos^2A(cos^2A + sin^2A)}{cos^2A}$

$cos^2A + sin^2A= 1$