Answer:
x = 63.57817848
x = 196.4218215
Step-by-step explanation:
cos 40 sin x - sin 40 cos x = 2/5
sin x cos 40 - cos x sin 40 = 2/5
Using trig identities sin(α – β) = sin(α) cos(β) – cos(α) sin(β)
sin ( x - 40) = 2/5
Rewriting as m = x-40
sin ( m) = 2/5
Taking the inverse sin of each side
sin ^-1 sin m = sin ^-1 (2/5)
m = 23.57817848
m = 180 -23.57817848 = 156.4218215
now find x
x -40 = m
x = m+40
x = 23.57817848 +40 = 63.57817848
x = 156.4218215 + 40 = 196.4218215
