Question

cos2 + tan2 - 1 / sin2 = tan2​

Answer 1

Answer:

$\frac{ { \cos( \alpha )}^{2} + { \tan( \alpha ) }^{2} - 1}{ \ \sin( \ { \alpha }^{2} ) }$

putting sin^2 theta + cos^2 theta instead of 1

$\frac{ { \cos( \alpha ) }^{2} + { \tan( \alpha ) }^{2} - { \cos( \alpha ) }^{2} - { \sin( \alpha ) }^{2} }{ { \sin( \alpha ) }^{2} }$

tan^2 theta - sin^2 theta/ sin^2 theta

$\frac{ { \tan( \alpha ) }^{2} }{ { \sin( \alpha ) }^{2} } - \frac{ { \sin( \alpha ) }^{2} }{ { \sin( \alpha ) }^{2} }$

$\frac{ { \sin( \alpha ) }^{2} }{ { \cos( \alpha ) }^{2} + { \sin( \alpha ) }^{2} } - 1$

$\frac{1}{ { \cos( \alpha ) }^{2} } - 1$

${ \sec( \alpha ) }^{2} - 1 = { \tan( \alpha ) }^{2}$

Hence PROVED!!!