# Identities

• Mar 16th 2010, 09:10 AM
kenzie103109
Identities
Complete the identity:

tan^2x - 3sinx tan x sec x

a) -2tan^2x
b) 1+cotx
c) sinx cscx
d) secx cscx
• Mar 16th 2010, 10:10 AM
masters
Quote:

Originally Posted by kenzie103109
Complete the identity:

tan^2x - 3sinx tan x sec x

a) -2tan^2x
b) 1+cotx
c) sinx cscx
d) secx cscx

Hi kenzie103109,

$\displaystyle \tan^2 x-3 \sin x \tan x \sec x=$

$\displaystyle \tan^2 x - \tan x\left(3 \sin x \frac{1}{\cos x}\right)=$

$\displaystyle \tan^2x - \tan x\left(3 \: \frac{\sin x}{\cos x}\right)=$

$\displaystyle \tan^2x - \tan x(3 \tan x)=$

$\displaystyle \tan^2 x-3 \tan^2x=$

$\displaystyle -2 \tan^2 x$
• Mar 16th 2010, 10:11 AM
Henryt999
Well
I understand the question to be:
$\displaystyle tan^2(x) -3\times sin(x)\times tan(x)\times sec(x)$
If I understood it correctly that is equal to:

$\displaystyle tan^2(x)-3\times sin(x)\times \frac{sin(x)}{cos(x)} \times \frac{1}{cos(x)}$
$\displaystyle tan^2(x)-3\times \frac{sin^2(x)}{cos^2(x)}$

equals:
$\displaystyle tan^2(x)-3tan^2(x) = -2tan^2(x)$