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If cos^2 A + cos^4 A = 1 then tan^2 A + tan^4 A is

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$\cos^2 A + \cos^4 A = 1 \\ \cos^4A = 1- \cos^2 A \\ \cos^4A = \sin^2 A \\\\ \frac{\cos^4A}{\sin^2A} =1 \\\\ \text{Now } \\\\ \tan^2 A + \tan^4 A = \tan^2 A(1 + \tan^2 A ) \\ = \tan^2 A \times \sec^2 A \\\\ = \frac{\sin^2 A }{\cos^4 A} =1$

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Ravindra Pindel

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