himpunan penyelesaian cos(x+75)°+cos(x-15)°=1/2√2 untuk 0°

[tex]rumus \\ \cos( \alpha ) + \cos( \beta ) \\ = 2 \cos \frac{1}{2} ( \alpha + \beta ) . \cos \frac{1}{2} ( \alpha - \beta ) \\ \\ \cos(x + 75) + \cos(x - 15) = ... \\ \\ = 2 \cos \frac{1}{2} (x + 75 + x - 15) . \cos \frac{1}{2} (x + 75 - (x - 15)) \\ \\ = 2 \cos \frac{1}{2} (2x + 60) . \cos \frac{1}{2} (90) \\ \\ = 2 \cos(x + 30) . \cos(45) \\ = 2 \cos(x + 30) .( \frac{1}{2} \sqrt{2} ) \\ \\ = \sqrt{2} \cos(x + 30) [/tex]
[tex] \sqrt{2} \cos(x + 30) = \frac{1}{2} \sqrt{2} \\ \\ \cos(x + 30) = \frac{1}{2} \\ \\ \cos(x + 30) = \cos(60) [/tex]
x + 30 = ±60 + k. 360
x =30 + k. 360 atau x = -90 + k. 360
interval = 0° < x < 360°

x = 30 + k. 360
untuk :
k = 0, x = 30°
k = 1, x = 390°

x = -90 + k. 360
untuk :
k = 0, x = -90°
k = 1, x = 270°
k = 2, x = 630°

Hp = {30°, 270°}