Prove Trig Identity: sec^6x - tan^6x = 1 + 3tan^2xsec^2x?

(sec^6x - tan^6x) = 1 + 3tan^2xsec^2x

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  • 10 years ago
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    LHS = sec^6x - tan^6x = (sec^2x - tan^2x)*(sec^4x + tan^4x + tan^2xsec^2x)

    = 1*[(sec^4x + tan^4x - 2tan^2xsec^2x) + (tan^2xsec^2x + 2tan^2xsec^2x)]

    = [(sec^2x - tan^2x)^2 + (3tan^2xsec^2x)]

    = 1 + 3tan^2xsec^2x

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