Sin(a-b), если Sina=8/17, Cosb=4/5, a u b- углы 1 четверти.

Question

Sin(a-b), если Sina=8/17, Cosb=4/5, a u b- углы 1 четверти.

Answer 1

Sin(a-b)=sinacosb-sinbcosa=8/17*4/5 - √(1-cos²b)*√(1-sin²a)=32/85-√(1-16/25)*√(1-64/289)=32/85-√9/25*√225/289=32/85-3/5*15/17=32/85-45/85=-13/85

Answer 2

Sin(a-b)=sina*cosb-sinb*cosa
cos^2a=1-64/289=225/289
cosa=15/17(т.к. 1 четверть)
sin^2b=1-16/25=9/25
sinb=3/5
sin(a-b)=8/17*4/5-3/5*15/17=32/85-45/85=-13/85