Question

已知sina=2/3,a∈(∏/2,∏),cosb=-3/4,b ∈(∏,3/2)，求cos(a+b)和cos(a－b)

Answer 1

sina=2/3,a∈(∏/2,∏)知cosa=-5^(0.5)/3
cosb=-3/4,b ∈(∏,3/2)，知sinb=-7^(0.5)/4
cos(a+b)=cosa*cosb-sina*sinb
cos(a-b)=cosa*cosb+sina*sinb

Answer 2

sina=2/3,a∈(∏/2,∏)
cosa=-√5/3
cosb=-3/4,b ∈(∏,3/2)，
sinb=-√7/4

cos(a+b)
=cosa*cosb-sina*sinb
=-√5/3*-3/4 +√7/4*2/3
=(3√5+2√7)/12

cos(a-b)
=cosa*cosb+sina*sinb
=-√5/3*-3/4 - √7/4*2/3
=(3√5-2√7)/12