Question

已知sinA=2sinB,tanA=3tanB,求证cos^2 A=3/8

Answer 1

sinA=2sinB (1)

tanA=3tanB (2)

(1)/(2)得

cosA=(2/3)cosB

即,3cosA=2cosB (3)

(1)^2+(3)^2得

sinA^2+9cosA^2=4

即,(1-cosA^2)+9cosA^2=4

所以,cosA^2=3/8