Question

Prove that cos (45-a) cos(45-b)- sin(45-a)sin(45-b)=sin (a+b)

Answer 1

$\cos(45 - a) \cos(45 - b) - \sin(45 - a) \sin(45 - b) \\ = \cos((45 - a) + (45 - b)) \: \: \\ used \: \: formula \: \: for \: \: \cos( \alpha + \beta ) \\ = \cos(90 - (a +b)) \\ = \sin( a + b )$