Question

cosecant of y plus cotangent of y times cosecant of y minus cotangent of y divided by cosecant of y.

-sin y

cos y

sin y

csc y

Answer 1

wow, that was kina hairy. Um so...

Answer 2

Thanks rob, it was right!

Answer 3

\[\left( \csc A+\cot A \right)\left( \csc A-\cot A\right)=\csc ^{2}A-\cot ^{2}A=1\]

Answer 4

Whhooaaaa.... way easier to do than that. Like @sujithayer points out, from the Pythagorean ID relating cosecant and cotangent, the num'r easily simplifies to 1.

So you have 1/csc(y)=sin(y)