the identity must be equal, you can manipulate both side of equation
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(1+csc(x))/(cot(x)+cos(x))=(sin(x)+1)/(cos(x)+sin(x)cos(x)) (multiplying top and bottom by sin(x)),

(sin(x)+1)/(cos(x)(1+sin(x))=1/cos(x)=sec(x) QED

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