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 1/2 A = 2 cos² A - 1 = 2 (1/√3)² - 1 = 2/3 - 1 = - 1/3
sin 1/2 A = √ (1 - cos² 1/2 A) = √ (1² - 1/3²) = √(1 - 1/9) =√8/9
sin1/2 A = 2/3 √3

tan 1/2 A = sin 1/2 A/ cos 1/2A =  (- 1/3)/ ( 2/3 √3)  = 1/(2 - √3)
tan 1/2 A = (2 + √3)