Prove that each of the following is an identity

I am frustated with these two problems, i can not figure them out, ive tried many identities but still no correct answer. (Thinking)

The problems are
#1.) (1+cot(x))^2-cot(x)=1/(1-cos(x))(1+cos(x))
#2.) 1-2cos^2(y)/1-2cos(y)sin(y)=sin(y)+cos(y)/sin(y)-cos(y)

please help or give some hints ,thank you .

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

Hello, starlet19!

The first one is not an identity . . . There must be a typo.

Quote:

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Multiply the right side by



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Ahhh, too fast for me, Calculus26!
.