Question

упростите выражение cos( a+b )+ sinasin b

Answer 1

cos(a+b) +sinasinb= cosacosb-sinasinb+sinasinb 
-sinasinb b и + sinasinb  сокращаются, и в итоге получается =cosacosb

Answer 2

cos(a+b) + sin(a)sin(b) = cos(a)cos(b) + sin(a)sin(b) + sin(a)sin(b)
= cos(a)cos(b) + 2sin(a)sin(b)
= cos(a)cos(b) + sin(2a) (using identity sin(2a) = 2sin(a)cos(a))
= cos(a)cos(b) + 2sin(a)cos(a) (using identity sin(2a) = 2sin(a)cos(a))
= cos(a)cos(b) + sin(2a) (using identity sin(2a) = 2sin(a)cos(a))