Question

Se cossecx=3/2, determine o valor do cos x

Answer 1

$\csc x = \dfrac{3}{2}\\ \sin x=\dfrac{2}{3}\\ \\ \cos x =\sqrt{1-\sin^2 x}\\ \\ \cos x =\sqrt{1-\left(\dfrac{2}{3} \right)^2}\\ \\ \cos x =\sqrt{1-\dfrac{4}{9}}\\ \\ \cos x =\sqrt{\dfrac{5}{9}} \\ \\ \boxed{\cos x =\dfrac{\sqrt{5}}{3}}$