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Prove the following trigonometric identities: sec^6 θ = tan^6 θ + 3tan^2 θsec^2 θ + 1

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Prove the following trigonometric identities:

sec6 θ = tan6 θ + 3tan2 θsec2 θ + 1

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Taking RHS 

tan6θ + 3tan2θsec2θ + 1 

= (sec2θ - 1)3 + 3(sec2θ - 1)sec2θ + 1 

[As, tan2θ = sec2θ - 1] 

= (sec6θ - 1 - 3sec4θ + 3sec2θ) + (3sec4θ - 3sec2θ) + 1 

[(a + b)3 = a3 - b3 - 3a2b + 3ab2] 

= sec6θ= LHS Hence Proved.

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