Simplifying $\cot^2(x)-\csc^2(x)$: 1

[karush]

Write
$\cot^2(x)-\csc^2(x)$
In terms of sine and cosine and simplify
So then
$\dfrac{\cos ^2(x)}{\sin^2(x)}
-\dfrac{1}{\sin^2(x)}
=\dfrac{\cos^2(x)-1}{\sin^2(x)}
=\dfrac{\sin^2(x)}{\sin^2(x)}=1$
Really this shrank to 1

Ok did these on cell so...

 

[Opalg]

Write
$\cot^2(x)-\csc^2(x)$
In terms of sine and cosine and simplify
So then
$\dfrac{\cos ^2(x)}{\sin^2(x)}
-\dfrac{1}{\sin^2(x)}
=\dfrac{\cos^2(x)-1}{\sin^2(x)}
=\dfrac{\sin^2(x)}{\sin^2(x)}=1$
Really this shrank to 1

Ok did these on cell so...

There is a minus sign missing (can you see where?).

 

[Greg]

\(\displaystyle \sin^2x+\cos^2x=1\)

\(\displaystyle 1+\cot^2x=\csc^2x\)

\(\displaystyle \cot^2x-\csc^2x=-1\)

 

[karush]

There is a minus sign missing (can you see where?).

ok i think the negative follows thru now
$\dfrac{\cos ^2(x)}{\sin^2(x)}
-\dfrac{1}{\sin^2(x)}
=-\dfrac{\cos^2(x)-1}{\sin^2(x)}
=-\dfrac{\sin^2(x)}{\sin^2(x)}=-1$