S=(100-90COSA)(100-90SINA) 已知 SINA+COSA=根号2* SIN(A+π） 求S的最大值

sinA+cosA = √2×sin(A+π) = -√2×sinA
cosA = -(√2+1)×sinA
由于|cosA|≤1,|sinA|≤1
可得：|sinA|≤√2-1
S/100=(10-9cosA)(10-9sinA)
=100-90(sinA+cosA)+81sinAcosA
=100-90(-√2×sinA) + 81sinA[-(√2+1)×sinA]
=100+90√2×sinA-81(√2+1)sin²A
=50(√2+1)-81(√2+1)[sinA-(10-5√2)/9]²
由于0

sinA+cosA = √2×sin(A+π) = -√2×sinA
cosA = -(√2+1)×sinA
由于|cosA|≤1，|sinA|≤1
可得：|sinA|≤√2-1
S/100=(10-9cosA)(10-9sinA)
=100-90(sinA+cosA)+81sinAcosA
=100-90(-√2×sinA) + 81sinA[-(...