Question

Prove that:
$\frac{1+cosecA}{cosecA} =\frac{cos^{2}A}{1-sinA}$

Answer 1

$\frac{1+cosecA}{cosecA} = \frac{ sin^{2}A }{1-sinA}$
L.H.S.:-
[tex]= \frac{ 1+ \frac{1}{sinA} }{ \frac{1}{sinA} } = \frac{ \frac{sinA+1}{sinA} }{ \frac{1}{sinA} } \\ = \frac{(1 + sinA)}{1} \times \frac{(1-sinA)}{(1-sinA)} \\ = \frac{1- sin^{2} A}{1-sinA} = \frac{ cos^{2}A }{1-sinA} = R.H.S.[/tex]

Hence, proved.