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+3t...