# Thread: Trig Identities - where is my error?

1. ## Trig Identities - where is my error?

Prove:
$\displaystyle csc(A)^2 + sec(A)^2 = csc(A)^2sec(A)^2$

left side is:
$\displaystyle (1/cos(A)^2) + (1/sin(A)^2)$

I multiply the first term by $\displaystyle (sin(A)^2)/(sin(A)^2)$
and the second term by $\displaystyle (cos(A)^2)/(cos(A)^2)$

$\displaystyle (sin(A)^2)/(sin(A)^2)(1/cos(A)^2) + (cos(A)^2)/(cos(A)^2)(1/sin(A)^2)$

Now the two terms have a common denominator and can be combined and we have:
$\displaystyle (sin(A)^2 + cos(A)^2)/(2cos(A)^2sin(A)^2)$

Then numerator = 1:
$\displaystyle 1/(2cos(A)^2sin(A)^2)$

Then we have
$\displaystyle (1/2)csc(A)^2sec(A)^2$

Where does the $\displaystyle 1/2$ come from? What am I doing wrong? How can I make the left side look like $\displaystyle csc(A)^2sec(A)^2$ ???

Thanx

-Tony

2. Hello Tony

Welcome to Math Help Forum!
Originally Posted by Xplorer
...

$\displaystyle (sin(A)^2)/(sin(A)^2)(1/cos(A)^2) + (cos(A)^2)/(cos(A)^2)(1/sin(A)^2)$

Now the two terms have a common denominator and can be combined and we have:
$\displaystyle (sin(A)^2 + cos(A)^2)/(2cos(A)^2sin(A)^2)$
Ouch! Since when have you added fractions like that?

$\displaystyle \frac{a}{b}+\frac{c}{b}=\frac{a+c}{b}$,
not $\displaystyle \frac{a+c}{2b}$.