Question

在三角形ABC中,若∠C=3∠B,求c/b的取值范围

Answer 1

正弦定理

c/b

＝sinC/sinB

=sin3B/sinB

=(sin3B)/sinB

=(sinBcos2B+sin2BcosB)/sinB =cos2B+2(cosB)^2

=3(cosB)^2-(sinB)^2

=3(cosB)^2+[1-(sinB)^2]-1

=4(cosB)^2 -2＋1

＝2cos2B＋1

C=3B

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