Hitung cos x jika cos x = tan x dengan x sudut lancip
DB45
Cos x = tan x cos x = sin x /cos x sin x = cos² x sin x = 1 - sin² x sin² x + sin x = 1 (sin x + 1/2)² = 1 + 1/4 =5/4 sin x + 1/2 = +_ 1/2√5 dan x lancip, sin x > 0
sin x = -1/2 + 1/2√5 --> sin² x = 3/2 - 1/2 √5 . cos x = √1- sin² x = √(1- 3/2 + 1/2 √5)=√(-1/2 + 1/2√5)
cos x = sin x /cos x
sin x = cos² x
sin x = 1 - sin² x
sin² x + sin x = 1
(sin x + 1/2)² = 1 + 1/4 =5/4
sin x + 1/2 = +_ 1/2√5 dan x lancip, sin x > 0
sin x = -1/2 + 1/2√5 --> sin² x = 3/2 - 1/2 √5
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cos x = √1- sin² x = √(1- 3/2 + 1/2 √5)=√(-1/2 + 1/2√5)