Find sin^4 (a) + cos^4 (a), if cos (a) + sin (a) = 1/3

49/81

Step-by-step explanation:

[cos (a) + sin (a) ]^2 = (1/3) ^2

(cos (a)) ^2 + 2sin (a) cos (a) + (sin (a)) ^2 = 1/9

(sin (a)) ^2 + (cos (a)) ^2 = 1

1 + 2sin (a) cos (a) = 1/9

2sin (a) cos (a) = - 8/9

sin (a) cos (a) = - 4/9

[cos (a) + sin (a) ]^4 = (1/3) ^4 = 1/81

(cos (a)) ^4 + 4sin (a) * (cos (a)) ^3 + 6 * (sin (a)) ^2 * (cos (a)) ^2 + 4 (sin (a)) ^3*cos (a) + (sin (a)) ^4 = 1/81

(cos (a)) ^4 + (sin (a)) ^4 + 4sin (a) cos (a) ((cos (a)) ^2 + (sin (a)) ^2) + 6 (sin (a) cos (a)) ^2 = 1/81

cos (a)) ^4 + (sin (a)) ^4 + 4sin (a) cos (a) (1) + 6 (sin (a) cos (a)) ^2 = 1/81

(cos (a)) ^4 + (sin (a)) ^4 + 4 (-4/9) + 6 ((-4/9) ^2) = 1/81

(cos (a)) ^4 + (sin (a)) ^4 - 16/9 + 6 (16/81) = 1/81

(cos (a)) ^4 + (sin (a)) ^4 = 1/81 + 16/9 - 6 (16/81)

(cos (a)) ^4 + (sin (a)) ^4 = 49/81