tentukan himpunan penyelesaian persamaan trigonometri berikut: cos(75-x) - cos(15-x) =0

-2 sin 1/2 (a+b) sin 1/2 (a-b) jadi

-2 sin 1/2 (75-x+15-x) sin 1/2 (75-x-15+x)

-2 sin 1/2(90 - 2x) sin 1/2 (60)

-2 sin (45-x) sin 30

- sin (45-X)

[tex]\cos(75-x)-\cos(15-x)=0 \\ \cos(75-x)-\sin(75+x)=0 \\ \cos 75\cos x+\sin 75\sin x-(\sin 75\cos x+\cos 75\sin x)=0 \\ \cos 75\cos x+\sin 75\sin x-\sin 75\cos x-\cos 75\sin x=0 \\ \sin x(\sin 75-\cos 75)-\cos x(\sin 75-\cos 75) \\ =0 \\ (\sin x-\cos x)(\sin 75-\cos 75)=0 \\ \sin x-\cos x=0 \\ \sin x=\cos x \\ \frac{\sin x}{\cos x}=1 \\ \tan x=1 \\ x=45^o+n.180^o, n\in B[/tex]