If $tan^4θ - tan^2θ = 1$ ; then $cot^4θ + cot^2θ = ?$

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Answer 1 · 2017-06-19T10:41:46

$cot^4 theta+cot^2theta=1$

$tan^4 theta-tan^2theta=1 or tan^4 theta=tan^2theta+1 or tan^4 theta = sec^2theta or sin^4 theta/cos^4 theta=1/cos^2theta$ or

$sin^4 theta/cos^2 theta=1 or cos^2theta/sin^4theta=1$

$cot^4 theta+cot^2theta=cot^2theta(1+cot^2theta)$

$= cot^2theta*csc^2theta= cos^2theta/sin^2theta*1/sin^2 theta$

$=cos^2theta/sin^4 theta= 1$

$:. cot^4 theta+cot^2theta=1$ [Ans]

If tan^4θ - tan^2θ = 1 tan^4θ - tan^2θ = 1 ; then cot^4θ + cot^2θ = ? cot^4θ + cot^2θ = ?