Question

$sin^{4}x+cos^{4}x=frac{7}{8}$

Answer 1

(sin^4(x) + cos^4(x) +2sin^2(x) cos^2(x) ) -2sin^2(x) cos^2(x) = 7/8

(sin ^2(x) + cos^2(x))^2   - 2sin^2(x) cos^2(x) = 7/8

1-2sin^2(x) cos^2(x) = 7/8

2sin^2(x) cos^2(x) = 1/8

sin^2(x) cos^2(x) = 1/16

2cos(4x)= 1

cos (4x) = 1/2

4x = +_ pi/3+2pin

x = +_ pi/12 + pin/2