请证明 secx^6-tanx^6=1+3tanx^2*secx^2

Question

请证明 secx^6-tanx^6=1+3tanx^2*secx^2

Answer 1

secx^6-tanx^6
=(sec^2-tan^2)(sec^4+sec^2tan^2+tan^4)
=sec^4+sec^2tan^2+tan^4
=sec^4-sec^2tan^2+tan^4-sec^2tan^2+3sec^2tan^2
=sec^2(sec^2-tan^2)+tan^2(tan^2-sec^2)+3sec^2tan^2
=sec^2 -tan^2+3sec^2tan^2
=1+3tan^2sec^2 不好意思,省略了所有x