Question

Proved that: cos² alpha - cos² bita/cos²alpha × cos² bita= tan²bita - tan²alpha​

Answer 1

$\frac{ { \cos }^{2} \alpha - { \cos}^{2} \beta }{ { \cos }^{2} \alpha { \cos }^{2} \beta } = \frac{ { \cos}^{2} \alpha }{ { \cos }^{2} \alpha { \cos }^{2} \beta } - \frac{ { \cos}^{2} \beta }{{ \cos }^{2} \alpha { \cos }^{2} \beta }$
$\frac{1}{ { \cos }^{2} \beta } - \frac{1}{ { \cos}^{2} \alpha }$
as you know that
${ \sin}^{2}theta + { \cos }^{2} theta = 1$
$\frac{{sin}^{2} \beta + {cos}^{2} \beta}{ {cos}^{2} \beta } - \frac{ {\sin }^{2} \alpha + { \cos }^{2} \alpha }{ {cos}^{2} \alpha }$
$\frac{ {sin}^{2} \beta }{ {{cos}^{2} }{ \beta } } + 1 \: - 1 - \frac{ {sin}^{2} \alpha }{ {cos}^{2} \alpha }$
${tan}^{2} \alpha - {tan}^{2} \beta$
hope it helps you thanks for asking these type of questions