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i have a question about trignometric identities.. it's realtivly easy, but am struggling with the algebra in it ( Algebra + trig = Very confusing to me )

Prove that ..

[Sinx/(1+Cosx)] + [(1+cosx) / sinx] = 2csc x

i manged to get it to [Sin

^{2}x+1+2cosx+cos

^{2}x] / SinxCosx

but i don't know what to do after that

any help would be appreciated, even if hints or steps without actually solving it for me .

Thank you