已知α,β∈(0,π/2),且2tanα+3sinβ=7,tanα-6sinβ=1,则sinα=

问题描述:

已知α,β∈(0,π/2),且2tanα+3sinβ=7,tanα-6sinβ=1,则sinα=

2tanα+3sinβ=7……(1),
tanα-6sinβ=1 ……(2)
(1)*2+(2): 5tanα=15===>tanα=3/1
∴sinα=3/[(√3²+1²)]=3/√10=3√10/10