Question

Qual o valor de cos²x/1-sen x??? Sen x = 1/3

Answer 1

(cos²x)/(1-sen x) = 
(1-sen²x)/(1-senx) = 
[1-(1/3)²] / (1-1/3) = 
(1-1/9) / (3/3 - 1/3) = 
(9/9-1/9)/ 2/3 = 
(8/9) / (2/3) = 
8/9 * 3/2 = 
(8*3)/(9*2) = 
24 / 18 = 4/3

Answer 2

$\mathrm{*}\ \textrm{Rela\c{c}\~ao fundamental}\ \to\ \mathrm{\sin^2{x}+\cos^2{x}=1}\\\\ \mathrm{\dfrac{\cos^2{x}}{1-\sin{x}}=\dfrac{1-\sin^2{x}}{1-\sin{x}}=\dfrac{(1+\sin{x})(1-\sin{x})}{(1-\sin{x})}=1+\sin{x}}\\\\ \mathrm{*\ Como\ \sin{x}=\dfrac{1}{3}\ \to\ 1+\sin{x}=1+\dfrac{1}{3}=\dfrac{3}{3}+\dfrac{1}{3}=\boxed{\mathbf{\dfrac{4}{3}}}}$