Question

Se cos x = 1/2 e 0 < x < π/2, qual é o valor da expressão

y = cossec x - sen x divido por sec x - cos x

?

Answer 1

cos x = 1/2 ⇒

x = π/3

y = (cossec π/3 - sen π/3) / (sec π/3 - cos π/3)

y = [ (1/sen π/3) - sen π/3] / [(1/cos π/3) - cos π/3]

y = [(1 - sen ² π/3)/ sen π/3] / [(1- cos ² π/3)/ cos π/3]

y = (cos ² π/3 / sen π/3) / ( sen ² π/3 / cos π/3)

y = (cos ² π/3 / sen π/3) . (cos π/3 / sen ² π/3)

y = cos ³ π/3 / sen ³ π/3

y = (1/2) ³ / (√3/2) ³

y = (1/8) / (3√3/8)

y = 1 / (3√3)

y = (√3)/9