Question

若a属于(0,派/4),B属于(0,派),且tan(a -B)=1/2,tanB=-1/7,则2a -B

Answer 1

tan2(a-B)

=2tan(a-B)/(1-tan²(a-B))

=2*(1/2)/(1-1/4)

=4/3,

tan(2a -B)

=tan[2(a-B)+B]

=tan2(a-B)tanB/(1-tan2(a+B)tanB)

=[4/3+(-1/7)]/[1-(4/3)(-1/7)]

=1,

由于a属于(0,π/4),2a属于(0,π/2)

B属于(0,π),由于tanB＜0,所以B属于(π/2,π)

则2a-B属于(-π,0),

所以2a -B =-3π/4.