Question

Para cosx = 1 , qual é o valor da expressão y= cossec x + sen x  ?
                   2                                                    cotg x . sec x

Answer 1

cos x = 1/2  --->   sen x = √3/2
cossec x = 1 ÷sen x -------> cossec x = 2/√3=2√3/3
cotg x = cos x ÷ sen x = √3/2 ÷ 1/2 = √3
sec x = 1 ÷ cos x----> sec x = 2

Substituindo:

$y=\frac{cossec x + sen x}{cotg x . secx}= \frac{\frac{2\sqrt3}{3}+\frac{\sqrt3}{2}}{\sqrt3.2}= \frac{\frac{4\sqrt3+3\sqrt3}{6}}{2\sqrt3}=\frac{\frac{7\sqrt3}{6}}{2\sqrt3}=\frac{7\sqrt3}{6}.\frac{1}{2\sqrt3}=\frac{7}{12}$