Sina+cosa=корень3/корень2 1/sin^4 a+1/cos^4 a =?

Question

Алгебра: Sina+cosa=корень3/корень2 1/sin^4 a+1/cos^4 a =?​

Anjik20125 · Answer

1 1
-- (cos6x + 4cos3x + 3) - -- (cos6x - 4cos3x + 3) =
8 8

1    1
= ( cos6x + 4cos3x + 3 - cos6x + 4cos3x - 3) = --- 8cos3x = cos3x
8    8

а сорь, там равно 1/2
Тогда, cos3x = 1/2
3x = +arccos1/2 + 2pk
3x = - arccos1/2 + 2pk

3x = pi/3 + 2pk
x1 = pi/9 + 2pk/3

x2 = -pi/9 + 2pk/3

Sina+cosa=корень3/корень2 1/sin^4 a+1/cos^4 a =?​