(1 - sin^{4} - cos^{4}) / cos^{4}

Question

(1 - sin^{4} - cos^{4}) / cos^{4}

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Answer 1

(1-sin^4(α)-cos^4(α))/cos^4(α)=(sin^4(α)+cos^4(α)+2sin^2(α)*cos^2(α)-(sin^4(α)+cos^4(α)))/cos^4(α)=(2sin^2(α)*cos^2(α))/cos^4(α)=2sin^2(α)*cos^2(α)/(cos^(α)*cos^2(α))=2sin^2(α)/cos^2(α)=2tg^2(α)