Question

Cos(a+b)cosb+ sin(a+b)sinb= cosa

Answer 1

Step-by-step explanation:

$\cos \: (a + b) \: cos \: b + \sin \: (a + b) \: sin \: b \\ = \cos \: a \\ LHS \\ = \cos \: (a + b) \: cos \: b + \sin \: (a + b) \: sin \: b \\ = \cos \{(a + b) - b \} \\ = \cos (a + b- b ) \\ = \cos \: a \\ = RHS \\ \\ formula \: used \\ \cos \:a \: cos \: b + \sin \: a \: sin \: b = \cos(a - b)$