Question

sec π / 6. cotg 2π / 3

Answer 1

$sec\frac{ \pi }{3} *cotg \frac{2 \pi }{3} = \frac{1}{cos \frac{ \pi }{3} }* \frac{ cos\frac{2 \pi }{3}}{sen \frac{2 \pi }{3} } = \frac{1}{cos \frac{ \pi }{3} } * \frac{-cos \frac{ \pi }{3} }{sen \frac{ \pi }{3} } =- \frac{1}{sen \frac{ \pi }{3} } =-cossec \frac{ \pi }{3}$

OBS:. 2π/3 ∈ 2° quadrante. Logo, o cosseno é negativo e o seno é positivo. 

cos2π/3 = -cos (π - π/3) = -cos(3π - 2π)/3 = - cosπ/3

sen2π/3 = sen(π - 2π/3) = sen (3π - 2π) = senπ/3