Question

Jika cos α = 1/3 dengan α sudut lancip, maka nilai dari tan 1/2 A adalah

Answer 1

Verified answer

Jawab

cos a = 1/3
cos a = 2 cos² 1/2 a - 1
2 cos² 1/2 a = cos a +1
cos² 1/2 a =  1/2 (cos a + 1) = 1/2 (1/3 +1) =  2/3
cos 1/2 a = √(2/3)

cos a = 1- 2sin² 1/2 a
2 sin² 1/2  a= 1 - cos a
sin² 1/2 a = 1/2 (1 - 1/3) = 1/3
sin 1/2 a = √(1/3)

tan 1/2 a = sin 1/2 a / cos 1/2 a =  (√(2/3) / (√(1/3)
tan 1/2 a = √2