Решение смотри в приложении
2(-2)+( 79/2) -2(-2)= 79/2= 39,5.
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
sinx * sin5x = cos4x
1/2(cos(x-5x) - cos(x+5x)) = cos4x
1/2( - cos4x - cos6x ) = cos4x
cos4x + cos6x + 2cos4x = 0
3cos4x + cos6x = 0
6cos(4x+6x)/2 cos(4x-6x)/2 = 0
6cos5x (-cosx)=0
6cos5x=0 или cosx = 0
5x = п/2 + пк, к ∈ z
x = п/10 + пк/5, к ∈ z
x = п/2, пк, к ∈ z