Question

Jika sin (x+30°) = sin x, buktikan tan x = 2 + √3 !
bantu jawab ya sobb =)

Answer 1

Sin (x+30) = sin x
sin x . cos 30 + cos x . sin 30 = sin x
sin x . (1/2)√3 + cos x . (1/2) = sin x

sin x - [ sin x . (1/2)√3 ] = cos x . (1/2)
sin x . [ 1 - (1/2)√3 ] = cos x . (1/2)
sin x / cos x = (1/2) / [1 - (1/2)√3]

tan x = 1 / (2 - √3)
*gunakan metode rasionalisasi penyebut. Diperoleh:
tan x = 2 + √3