3sec^2thetatan^2theta+1=sec^6theta-tan^6theta
Right Side=sec^6theta-tan^6theta
=(sec^2theta)^3-(tan^2theta)^3->use difference of two cubes formula
=(sec^2theta-tan^2theta)
(sec^4theta+sec^2thetatan^2theta+tan^4theta)
=1 *(sec^4theta+sec^2thetatan^2theta+tan^4theta)
=sec^4theta+sec^2thetatan^2theta+tan^4theta
=sec^2theta sec^2 theta+sec^2thetatan^2theta+tan^2theta tan^2 theta
=sec^2theta(tan^2theta+1) +sec^2thetatan^2theta+tan^2theta(sec^2theta-1)
=sec^2thetatan^2theta+sec^2theta+sec^2thetatan^2theta+sec^2thetatan^2theta-tan^2theta
=sec^2thetatan^2theta+sec^2thetatan^2theta+sec^2thetatan^2theta+sec^2theta-tan^2theta
=3sec^2thetatan^2theta +1
= Left Side