Question

已知COS(A+π/4)=3/5,则SIN2A？

Answer 1

COS(A+π/4)=3/5所以sin(A+π/4)=4/5,((COS(A+π/4))^2+（sin(A+π/4)）^2=1)由此可求得cosA=7√2/10,sinA=√2/10.所以SIN2A=2sinAcosA=7/25

Answer 2

cos(A + π/4) = 3/5
cosAcos(π/4) - sinAsin(π/4) = 3/5
(1/√2)(cosA - sinA) = 3/5
(cosA - sinA)² = (3√2/5)²
cos²A + sin²A - 2sinAcosA = 18/25
1 - sin2A = 18/25
sin2A = 7/25