Sec4theta - sec2theta = tan4theta +tan2theta
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Sec4theta - sec2theta
= sec2theta(sec2theta - 1)
= ( 1 + tan2theta)( 1/cos2theta - 1)
= 1 + tan2theta * ( 1 - cos2theta / cos2theta )
= 1+ tan2theta * sin2theta/
= 1 + tan2theta * tan2theta
= tan2theta + tan4theta.
= sec2theta(sec2theta - 1)
= ( 1 + tan2theta)( 1/cos2theta - 1)
= 1 + tan2theta * ( 1 - cos2theta / cos2theta )
= 1+ tan2theta * sin2theta/
= 1 + tan2theta * tan2theta
= tan2theta + tan4theta.
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