If sin A= 1/ root (10) sin B= 1/root (5) ( A, B and A+ B being positive acute angles, show that A+B= pie/4.

If sin A = 1 / ( 10 ) ^{( 1 / 2 )}and sin B = 1 / ( 5 ) ^{( 1 / 2 )} then cos A = ( 1 - sin ² A ) ^{( 1 / 2 )}

= cos A = 3 / ( 10 ) ^{( 1 / 2 )} ,similarly ,cos B = ( 1 - sin² B )^{(1 / 2 )}

= cos B = 2 / ( 5 ) ^{( 1 / 2 )}

= sin ( A + B ) = sin ( pi / 4 )

= sin A cos B + sin B cos A = sin ( pi / 4 )

substitute the values of sin A , cos A , cos B and sin B that we have obtained earlier and you'll get the desired result.