(1+cosx/sinx)+(sinx/1+cosx) = 2cscx
get a common denominator
(1 + cosx)(1 + cosx) +(sinx)(sinx) = 2 cscx
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sinx (1 + cosx)
1 + 2cosx + (cosx)^2 + (sinx)^2 = 2 cscx
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sinx(1 + cosx)
1 + 2cosx + 1 = 2
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sinx(1 + cosx) sinx
2 + 2cosx = 2
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1 + cosx
2(1+cosx) = 2
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1 + cosx
2 = 2