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\frac{sin  \beta + cos \beta  -1}{sin \beta -cos \beta +1} = \frac{cos \beta} {1+sin \beta }\\ \\ cross-multiply\\ (sin \beta + cos \beta -1)(1+sin \beta) = (sin \beta -cos \beta +1)cos \beta \\ \\ LHS = sin \beta +sin^2 \beta +cos \beta +cos \beta sin \beta -1-sin \beta \\RHS = sin \beta cos \beta -cos^2 \beta +cos \beta \\ \\ LHS = (sin^2 \beta -1) + cos \beta + cos \beta sin \beta = -cos^2 \beta +cos \beta + sin \beta cos \beta \\ \\ = RHS\\ 
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sir but you have to prove it not to show
IT will be the same procedure and steps. Multiply given fraction by (1+sinB)in numerator and denominator. (sin B+CosB-1)(1+sinB) = expand and simplify to get cosB-cos squareB+sinB cosB . Take cos B as a factor. cancel common factor in numerator and denominator. we get the answer.
thanx n u r welcom saurabh