Question

show that tan^2teta+tan^4teta=sec^4teta-sec^2 teta​

Answer 1

take the LHS

$tan^{4}$∅+$tan^{2}$∅

$tan^{2}$∅(1+$tan^{2}$∅) .          ⇒ 1

we know that,

$1+tan^{2}$∅ = $sec^{2}$∅

therefore from 1

($sec^{2}$∅-1)$sec^{2}$∅

$sec^{4}$∅ - $sec^{2}$∅

thus LHS = RHS