Question

Sin(п\3-а)+cos(п\6-а) выражение cos x - корень из3 sin x=1 решить уравнение решите

Answer 1

1)  sin(π/3 - α) + cos(π/6 - α) = sin(π/3)*cosα - cos(π/3)*sinα + cos(π/6)*cosα + sin(π/6)*sinα =(√3/2*)cosα - (1/2)*sinα + (√3/2)*cosα + (1/2)*sinα = 
= (√3)*cosα
2)  cosx - √3sinx = 1  делим на 2
(1/2)*cosx - (√3/2)*sinx = 1/2
cos(π/3)cosx - sin(π/3)*sinx = 1/2
cos(π/3 + x) = 1/2
x + π/3 = (+ -)*arccos(1/2) + 2πn, n∈Z
x + π/3 = (+ -)*(π/3) + 2πn, n∈Z
x  = (+ -)*(π/3) - π/3 + 2πn, n∈Z