Question

已知x是第三象限角,且sin4x+cos4x=九分之七,求sin2x的值

Answer 1

sin^4 X+cos^4 X=7/9,

sin^4 X+cos^4 X+2sin^2Xcos^2X-2sin^2Xcos^2X=7/9,

(sin^2X+cos^2X)^2-2sin^2Xcos^2X=7/9

1-1/2*(sin2x)^2=7/9

(sin2x)^2=4/9

因为X为第三象限的角,即2kπ+π