Question

tan^2sec^2 (90-a) - sin^2A cosec^2 (90-A)=1

Answer 1

[tex]sec^{2} (90 - A) = cosec^{2}A \\ cosec^{2}(90 - A) = sec^{2}A [/tex]
Therefore, the given equation can be written as:
$tan^{2}Acosec^{2}A - sin^{2}Asec^{2}A$ = $tan^{2}Acosec^{2}A - \frac{sin^{2}A}{cos^{2}A}$
= [tex]tan^{2}Acosec^{2}A - tan^{2}A [/tex]
= $tan^{2}A(cosec^{2}A - 1)$
= $tan^{2}A(cot^{2}A)$
=$tan^{2}A(\frac{1}{tan^{2}A})$
=1