Question

Tentukan himpunan penyelesaian sin (x+phi/4) - sin (x-phi/4) = 1 dalam selang 0< x < 2phi

Answer 1

Verified answer

Sin(x+π/4)-sin(x-π/4) = 1
2 cos(x+π/4+x-π/4)/2 sin(x+π/4-x+π/4)/2
2 cos(2x)/2 sin(2π/4)/2
2 cos(x) sin(π/4) = 1
cos(x) sin(π/4) = 1/2
cos(x) sin(45°) = 1/2
cos(x) 1/2√2 = 1/2
cos(x) = 1/2 / √2/2
cos(x) = 1×2/2√2 = 2/2√2 = 1/√2
cos(x) = 1/2 √2
arccos 1/2√2 = 45°,315°
HP={45°,315°}