证明：sin(2α+β)=5sinβ
证：
sin(2a+b)/sinb
=sin[(a+b)+a]/sin[(a+b)-a]
=[sin(a+b)*cosa+sina*cos(a+b)]/
[sin(a+b)*cosa-sina*cos(a+b)]
分子,分母同时除以cos(a+b)*cosa得
sin(2a+b)/sinb
=[tan(a+b)+tana]/[tan(a+b)-tana]
由3tana=2tan(a+b)
则tana=2/3*tan(a+b)
则sin(2a+b)/sinb
=[tan(a+b)+2/3*tan(a+b)]/[tan(a+b)-2/3*tan(a+b)]
=[5/3*tan(a+b)]/[1/3*tan(a+b)]
=5
所以
sin(2α+β)=5sinβ