How do you verify the identity #3sec^2thetatan^2theta+1=sec^6theta-tan^6theta#?

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Answer 1 · 2016-10-03T18:23:37

See below

#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