1)
sin x + cos x = 2/5 square both sides
sIn^2 x + 2sin(x)cos(x) + cos^2x = 4/25
(sin^2 x + cos^2 x) + 2sin(x)cos(x) = 4/25
(1) + 2sin (x) cos(x) = 4/25 subtract 1 from both sides
2sin(x)cos(x) = 4/25 -1
2sin(x)cos(x) = -21/25 divide both sides by 2
sin(x) cos(x) = -21/50 square both sides
sIn^2x cos^2x = 441/2500
sin^2 x ( 1 - sin^2x) = 441/2500
sin^2x - sin^4x = 441/2500
sin^4x = sin^2x -441/2500 (1)
sin^2 x cos^2 x = 441/2500
(1 - cos*2x) (cos^2x) = 441/250
cos^2x - cos^4x = 441/2500
cos^4x = cos^2x - 441/2500 (2)
Add (1) and (2)
sin^4 x + cos^4x = ( sin^2 x + cos ^2 x ) - 441/2500 - 441/2500
sin^4x + cos ^4 x = (1) - 882/2500
sin^4 x + cos ^4x = [2500 -882 ] / 2500
sin^4 x + cos ^4 x = 1618 /2500 = 809 / 1250