Question

已知α属于(-π/2,0),cosα =4/5,则tan2α=?

Answer 1

tan2α = sin2α/cos2α = 2sinα*cosα/(cosα*cosα-sinαsinα)

α属于(-π/2,0) ==> sinα = -(1-cosα*cosα)^(1/2) = -(1- (4/5)^2)^(1/2) = -3/5

==> tan2α = (2 * (-3/5) * 4/5)/((4/5)^2 - (-3/5)^2)

= (-24/25) / (7/25) = -24/7