已知：sinβ=1/3，sin(a+β)=1，求sin(2a+β)．
由sin(a+β)=1可知a+β=2kπ+π/2(k∈z)而2a+β=2(a+β)-β=2(2kπ+π/2)-β=4kπ+π-β所以sin(2a+β)=sin(4kπ+π-β)=sin(π-β)=sinβ=1/3
已知：sinβ=1/3，sin(a+β)=1，求sin(2a+β)．
由sin(a+β)=1可知a+β=2kπ+π/2(k∈z)而2a+β=2(a+β)-β=2(2kπ+π/2)-β=4kπ+π-β所以sin(2a+β)=sin(4kπ+π-β)=sin(π-β)=sinβ=1/3
