2. Jika cos x – sin x = 1/2, tentukan nilai dari tan 2x
1. Jika cos ( x + 45° ) = cos x, hitunglah nilai dari tan x
1. cos (x+45) = cos x
cos x.cos 45 – sin x.sin 45 = cos x
(1/2).√2.cos x – (1/2).√2.sin x = cos x
cos x.((1/2).√2 – 1) = (1/2).√2.sin x
sin x/cos x = ((1/2).√2 – 1)/(1/2).√2
tan x = 1 – 2/√2
tan x = 1 - √2
2. cos x – sin x = 1/2, kuadratkan masing2 sisi
cos² x + sin² x – 2.sin x.cos x = 1/4
1 – sin 2x = 1/4
sin 2x = 1-(1/4)
sin 2x = 3/4
cos 2x = (√4²-3²)/4
cos 2x = (√7)/4
tan 2x = sin 2x/cos 2x
= 3/√7
= (3/7).√7