Question

cscU -1/cscU+1= 1-sinU/1+sinU

Answer 1

Trying to find the identities

Answer 2

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Answer 3

Since csc(u) = 1/sin(u) and cot(u) = cos(u)/sin(u), we have...

LHS
= (1/sin(u)) - cos(u)/(sin(u))
= (1 - cos(u))/sin(u)

Then, multiply the top and bottom by 1 + cos(u) to get...

(1 - cos(u))/sin(u) * (1 + cos(u))/(1 + cos(u))
= (1 - cos²(u))/(sin(u)(1 + cos(u)))
= (1 - cos²(u))/(sin(u)(1 + cos(u)))

Finally, by noting that 1 - cos²(u) = sin²(u), we can simplify the expression to...

sin²(u)/(sin(u)(1 + cos(u)))
= sin(u)/(1 + cos(u))
= RHS

Hope this helped! :D