Question

Determine o valor de cossec x - sen x . Sabendo que se cos x = 1/2 (0º a 90º )

Answer 1

$\boxed{\begin{array}{l}\sf cos(x)=\dfrac{1}{2}\implies cos^2(x)=\dfrac{1}{4}\\\sf sen^2x=\dfrac{4}{4}-\dfrac{1}{4}=\dfrac{3}{4}\\\sf sen(x)=\dfrac{\sqrt{3}}{\sqrt{4}}=\dfrac{\sqrt{3}}{2}\\\sf cossec(x)=\dfrac{2}{\sqrt{3}}=\dfrac{2\sqrt{3}}{3}\\\sf cossec(x)-sen(x)=\dfrac{2\sqrt{3}} {3}-\dfrac{\sqrt{3}}{2}\\\sf cossec(x)-sen(x)=\dfrac{4\sqrt{3}-3\sqrt{3}}{6}\\\sf cossec(x)-sen(x)=\dfrac{\sqrt{3}}{6}\end{array}}$