Question

Verify the identity:

cos(a+B)/cos a sin B = cot B -tan a

Answer 1

cos( A + B ) = cosAcosB - sinAsinB ;
cos( A + B ) / ( cosAsinB ) = ( cosAcosB - sinAsinB ) / ( cosAsinB ) = ( cosAcosB ) / ( cosAsinB ) - ( sinAsinB ) / ( cosAsinB ) = cosB / sinB - sinA / cosA = cotB - tanA ;