Simplify the following expression : $\frac{1-sinA}{cosA}+\frac{cosA}{1-sinA}$

2secA

$\frac{1-sinA}{cosA}+\frac{cosA}{1-sinA}$

= \(\frac{( 1 -sinA)² + cos²A }{cosA(1-sinA)}\)

= \(\frac{( 1 + sin²A - 2sinA) + cos²A }{cosA(1-sinA)}\)

{ using , sin²A + cos²A = 1 }

= \(\frac{( 1 + 1  - 2sinA) }{cosA(1-sinA)}\)

= \(\frac{2( 1  - sinA) }{cosA(1-sinA)}\)

= \(\frac{2 }{cosA}\)

= 2secA