Question

Sec^2 theta + cosec^2 theta = sec^2 theta x cosec^2 theta

Answer 1

Step-by-step explanation:

${ \sec( \alpha ) }^{2} + { \csc( \alpha ) }^{2}$

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

Here,

Take LCM

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

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

${ \sec( \alpha ) }^{2} \times { \csc( \alpha) }^{2}$