Question

Hitunglah nilai [cos (4/3)pi - tan(3/4)pi]^2 - sec(1/3)pi

Answer 1

Pi = 180°
cos 4/3 pi = cos 240 = cos (180-60)= - cos 60 = -1/2√3
tan 3/4pi = tan 135 = tan(180-45) = tan 45 = 1
sec 1/3 pi = sec 60 = 1/cos 60 = 1/(1/2 ) = 2

[ cos 4/3 pi - tan 3/4 pi]^2 - sec 1/3 pi =
= (-1/2√3 - 2)² - (2)
= 3/4 + 2√3 + 4 - 2=
= 3/4 + 2√3 + 2
= 1/4 ( 3 + 8√3 + 8)
= 1/4 (11 + 8√3)