Simplify the following expression : $\frac{1-sinA}{cosA}+\frac{cosA}{1-sinA}$
Answer & explanation
Correct answer: option 3
$\frac{1-sinA}{cosA}+\frac{cosA}{1-sinA}$
= \(\frac{( 1 -sinA)² + cos²A }{cosA(1-sinA)}\)
= \(\frac{( 1 + sin²A - 2sinA) + cos²A }{cosA(1-sinA)}\)
{ using , sin²A + cos²A = 1 }
= \(\frac{( 1 + 1 - 2sinA) }{cosA(1-sinA)}\)
= \(\frac{2( 1 - sinA) }{cosA(1-sinA)}\)
= \(\frac{2 }{cosA}\)
= 2secA