Chứng minh rằng tan^2x + cot^2x = 6+2cos4x/1-cos4x
Giải thích
tan2x + cot2x = sin2xcos2x+cos2xsin2x=sin4x+cos4xsin2x.cos2x
= sin2x+cos2x−2sin2x.cos2xsin2x.cos2x
= 1−2sin2x.cos2xsin2x.cos2x
= 1−12sin22x14sin22x
= 1−12.1−cos4x214.1−cos4x2
= 1−14.1−cos4x18.1−cos4x
= 8−2+2cos4x1−cos4x
= 6+2cos4x1−cos4x
Vậy tan2x + cot2x = 6+2cos4x1−cos4x