tanα=-2.∴sinα/cosα=-2 ∴sinα=-2cosα∵sin²α+cos²α=1∴(-2cosα)²+cos²α=1∴5cos²α=1∴cos²源掘α=1/5∴cosα=√5/5∵sin²α=1-1/5=4/5∴sinα=(态卜2√5)/5sin(α+π/6) =sinαcosπ/6+cosαsinπ/6=(2√雹闭核5)/5×(√3/2)+(√5)/5×(1/2)=(2√15+√5)/10