Question

高一数学二倍角与半角的正弦、余弦和正切的问题

Answer 1

1 (sinA+cosA)^2=49/25

(sinA)^2+(cosA)^2+2sinAcosA=49/25

sin2A=49/25-1=24/25

cos2A=正负√[1-(sin2A)^2]=正负7/25

2 cos(A+B)cos(A-B)

=(cosAcosB-sinAsinB)(cosAcosB+sinAsinB)

=(cosAcosB)^2-(sinAsinB)^2

=(cosAcosB)^2-[1-(cosA)^2][1-(cosB)^2]

=(cosA)^2+(cosB)^2-1=1/4

既(cosA)^2+(cosB)^2=5/4