Question

Simplify the expression (cscy+coty)(cscy-coty)/cscy

Answer 1

first off the numerator is
\[\csc^2(y)-\cot^2(y)\] after you multiply

Answer 2

then we need some identity for the numerator
starting with the well known
\[\cos^2(x)+\sin^2(x)=1\] we can get both \(\cot^(x)\) and \(\csc^2(x)\) by dividing through by
(\sin^2(x)\) to get
\[\cot^2(x)+1=\csc^2(x)\] or
\[\csc^2(x)-\cos^2(x)=1\]

Answer 3

typo there i meant
\[\csc^2(x)-\cot^2(x)=1\]

Answer 4

so the numerator is 1 you get
\[\frac{1}{\csc(y)}=\sin(y)\]

Answer 5

thanks