Why is -csc^2 (pi/4) = -2 ?

Question

anonymous · Answer

$$cosec (\pi/4)= 1/ \sin (\pi/4)= 1/(1/\sqrt (2))=\sqrt(2)
\[cosec(\pi/4)^2= \sqrt(2)*\sqrt(2)=2$$
$$-cosec^2(\pi/4)=-2$$

anonymous · Answer

Let me make sure I understand; cosecant sqaured of pi/4 is equal to 1 divided by sin squared of pi/4 , and sin (pi/4 )is [square root 2 divided by 2] . so, [ (1)/(sqrt 2/2)] is a complex fraction resulting in 1 over 1 times 2 over sqrt 2 , simplfying to sqrt2. I'm confused after this point and all the symbols in your explanation are throwing me off a bit. Can you help me?

anonymous · Answer

First, see that csc is reciprocal of sin. Find sin(π/4).
Take the reciprocal of that to get csc(π/4).
Then square that to get csc^2.
Finally, tack on a negative sign.

anonymous · Answer

Ohh!!! Okay, wow, I know why I was thrown off, I used sin(π/4) but did not reciprocate it for csc. That was my mistake, thank you to both of you!!!

anonymous · Answer

n.p.