Question

Sec^4theta-sec^2theta=tan^4+tan^2theta

Answer 1

To Proove : sec⁴∅ - sec²∅ = tan⁴∅ + tan²∅


Proof :


sec⁴∅ - sec²∅

( sec²∅ × sec²∅ ) - sec²∅

sec²( sec² - 1 )


We know,
sec²A - 1 = tan²A


sec²∅ ( tan²A )


We know,
sec²A = tan²A + 1


( tan²∅ + 1 ) ( tan²∅ )

tan⁴∅ + tan²∅



Proved.

$\:$

Answer 2

To Proove : sec⁴A - sec²A= tan⁴A + tan²A


Proof :




sec⁴A- sec²A


( sec²A × sec²A ) - sec²A


sec²( sec² - 1 )



$<b>sec²A - 1 = tan²A$ $</b>$



sec²A ( tan²A )



$<b>$
sec²A = tan²A + 1
$</b>$



( tan²A + 1 ) ( tan²A )


tan⁴A + tan²A



Proved.

$\:$