How to prove this identity?

Question

Hint: factor the left side first

#2sec^2(theta)tan^2(theta)-tan^4(theta)=sec^4(theta)-1#

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Answer 1 · 2017-11-17T03:46:39

#LHS=2sec^2(theta)tan^2(theta)-tan^4(theta)#
#=2sec^2(theta)(sec^2(theta)-1)-(sec^2(theta)-1)^2#

#=2sec^4(theta)-2sec^2(theta)-(sec^4(theta)-2sec^2(theta)+1)#

#=2sec^4(theta)-2sec^2(theta)-sec^4(theta)+2sec^2(theta)-1#

#=sec^4(theta)-1=RHS#