Question

plz anser it fast .. with solution

Answer 1

Heya

We know, for a 2x2 matrix with labels a,b,c,d :

$| \binom{a}{c} \binom{b}{d} | = (ac - bd)$

Hence, we calculate the determinant as :

$= { \cos }^{2} ( \frac{ \alpha }{2} ) { \cos }^{2} ( \frac{ \beta }{2} ) - { \sin }^{2} ( \frac{ \alpha }{2} ){ \sin }^{2} ( \frac{ \beta }{2} )$

$= \cos( \frac{ \alpha + \beta }{2} )$
Since the two angles is complimentary, sum of angles is 90°

Hence, the Value :
$= \cos( \frac{ \alpha + \beta }{2} ) = \cos( {45}^{0} ) = \frac{1}{ \sqrt{2} }$


Thus, we conclude that only (2) is correct.