Question

化简4*sin(arcsin(3/5)-arcsin(3/10)),

Answer 1

设arcsin(3/5)=α∈(0,π/2)

,则sinα=3/5,cosα=4/5

设arcsin(3/10）=β∈（0,π/2）

则sinβ=3/10,cosβ=√91/10

∴4*sin(arcsin(3/5)-arcsin(3/10))

=4sin(α-β)

=4(sinαcosβ-cosαsinβ)

=4(3/5*√91/10-4/5*3/10)

=4(3√91-12)/50

=(6√91-24)/25