For # 2 multiply the top and bottom by sin(y) -cos(y)

expand and use sin^2(y) +cos^2(y) =1

For # 1 I'm not sure it is an identity since the right hand side

is csc^2(x) = cot^2(x) + 1 and if you expand the left hand side you get

cot^2(x) +2cot(x) +1 -cot(x) = cot^2(x) +cot(x) +1