Sin(π/4-a),если sina=корень из двух/3 и π/2 меньше а меньше π.

г) (1-9y²) / (3y²-13+4) = (1+3y)(1-3y) / 3(y-4)(y-1/3) = 3(1/3+y)(1/3-y) / 3(y-4)(y-1/3) = (1/3+y)(1/3-y) / (y-4)(y-1/3)

3y²-13+4 = 0;

D = (-13)²-4*3*4 = 169-48 = 121, √D = 11

y₁ = (13+11) / 2*3 = 24/6 = 4

y₂ = (13-11) / 2*3 = 2/6 = 1/3

Значит: 3y²-13+4 = 3(y-4)(y-1/3)

д) (36a²-12a+1) / (6a²+11a-2) = 36(a-1/6)(a-1/6) / 6(a-1/6)(a+2) = 6(a-1/6) / (a+2)

36a²-12a+1 = 0;

D = (-12)²-4*36*1 = 144-144 = 0, √D = 0

a = 12/(2*36) = 12/72 = 1/6

Значит: 36a²-12a+1  = 36(a-1/6)(a-1/6)

6a²+11a-2 = 0;

D = 11²-4*6*(-2) = 121 + 48 = 169, √D = 13

a₁ = (-11+13) / 2*6 = 2/12 = 1/6

a₂ = (-11-13) / 2*6 = -24/12 = -2

Значит: 6a²+11a-2 = 6(a-1/6)(a+2)

x = πk/4 - π/48

x = 3π/4  + πk

Объяснение:

cos3x - sin5x = √3 (cos5x + sin3x)

cos3x - sin5x = √3 cos5x + √3 sin3x

cos3x - √3 sin3x  = sin5x + √3 cos5x

2*(1/2cos3x - √3/2 sin3x ) = 2*(1/2sin5x + √3/2 cos5x)

1/2cos3x - √3/2 sin3x = 1/2sin5x + √3/2 cos5x

sin(30° - 3x) = sin(5x + 60°)

sin(30° - 3x) - sin(5x + 60°) = 0

2sin( ((30° - 3x) - (5x + 60°))/2)*cos(((30° - 3x)+ (5x + 60°))/2) = 0

2sin(-4x-15°)cos(-x + 45°) = 0

-2sin(4x + π/12)cos(x - π/4) = 0

1) sin(4x + π/12) = 0

4x + π/12 = πk

4x = πk - π/12

x = πk/4 - π/48

2) cos(x - π/4)  = 0

x - π/4 = π/2 + πk

x = π/2 + πk + π/4

x = 3π/4  + πk